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biology.md

Everything biology related...

Biology

  • Hernan G. Garcia, Jané Kondev, Nigel Orme, Julie A. Theriot, Rob Phillips, "A First Exposure to Statistical Mechanics for Life Scientists". arXiv:0708.1899
  • Alex H. Lang, Charles K. Fisher, Thierry Mora, Pankaj Mehta, "Thermodynamics of statistical inference by cells". arXiv:1405.4001

DNA

  • Cristian Micheletti, Marco Di Stefano, Henri Orland, "The unknotted strands of life: knots are very rare in RNA structures". arXiv:1410.1549
  • Sandro Bottaro, Francesco Di Palma, Giovanni Bussi, "The Role of Nucleobase Interactions in RNA Structure and Dynamics". arXiv:1410.1271
  • C. Manuel Carlevaro, Ramiro M. Irastorza, Fernando Vericat, "Quaternionic representation of the genetic code". arXiv:1505.04656
  • Elisabeth Rieper, Janet Anders, Vlatko Vedral "Quantum entanglement between the electron clouds of nucleic acids in DNA". arXiv:1006.4053
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gr-qc.md

Everything related to (classical & quantum) gravity and quantum cosmology.

Classical Gravity

  • V. Bozza, "Alternatives to Schwarzschild in the weak field limit of General Relativity". Eprint arXiv:1502.05178

Mathematical Theorems

  • Alan D. Rendall, "Theorems on existence and global dynamics for the Einstein equations". arXiv:gr-qc/0505133
  • Edward Witten, "Light Rays, Singularities, and All That". arXiv:1901.03928, 99 pages

Energy Conditions

We would like the stress-energy tensor in GR to satisfy the basic intuition that "energy should be positive". Without any such condition, it is impossible to write down any singularity theorem.

This involves examining the sign of a scalar obtained by contracting the stress-energy tensor T_{\mu\nu} with future time-like or light-like vectors x^{\mu}. There are 4 possible conditions:

  1. Weak
  2. Dominant = Weak + extra condition
  3. Strong (independent of either weak or dominant conditions)
  4. Null = Strong + extra condition = Dominant + extra condition
  • Erik Curiel, "A Primer on Energy Conditions". arXiv:1405.0403, 52 pages.
  • Maulik Parikh, "Two Roads to the Null Energy Condition". arXiv:1512.03448, 11 pages.

Solutions which satisfy energy conditions

  • Paul Tod, "Asymptotically $AdS_2\times S^2$ metrics satisfying the Null Energy Condition". arXiv:1809.01374, 17 pages

Symmetries

  • Casey Cartwright, Alex Flournoy, "Background-Independence from the Perspective of Gauge Theory". arXiv:1512.03808, 6 pages.

BMS Symmetries

For asymptotically flat spacetime, we expect to recover something that "looks like" Poincare symmetry "at" spatial infinity. It turns out we do get symmetries, a group called the BMS (Bondi-Metzner-Sachs) group. It turns out to be surprisingly useful for many qualitative statements. Hawking claims to have "solved" the information paradox using BMS symmetries. As far as I know, this has been studied in 3 and 4 dimensions.

  • Carles Batlle, Victor Campello, Joaquim Gomis, "Canonical Realization of BMS3". arXiv:1703.01833, 23 pages.
  • Temple He, Vyacheslav Lysov, Prahar Mitra, Andrew Strominger, "BMS supertranslations and Weinberg's soft graviton theorem". arXiv:1401.7026, 14 pages.
  • Thomas Mädler, Jeffrey Winicour, "Bondi-Sachs Formalism". arXiv:1609.01731, 31 pages. Good introduction to the ambient formalism for discussing BMS symmetries.
  • Andrew Strominger, Alexander Zhiboedov, "Gravitational Memory, BMS Supertranslations and Soft Theorems". arXiv:1411.5745, 18 pages.

Related Symmetries

  • D. D. McNutt, M. T. Aadne, "I-Preserving Diffeomorphisms of Lorentzian Manifolds". arXiv:1901.04728, 20 pages

In 2+1 dimensions

  • Blagoje Oblak, "BMS Particles in Three Dimensions". arXiv:1610.08526, 437 pages.
  • Glenn Barnich, Blagoje Oblak, "Notes on the BMS group in three dimensions: I. Induced representations". arXiv:1403.5803, 33 pages
  • Glenn Barnich, Blagoje Oblak, "Notes on the BMS group in three dimensions: II. Coadjoint representation". arXiv:1502.00010, 22 pages.

Censorship Hypothesis

Weak Form. The only singularities are either black holes or the Big Bang, and black holes are "protected" by an "armour" we call the event horizon. Anything underneath that armour "cannot be seen".

Strong Form. GR is a classical field theory, hence it is "deterministic" in the sense that given initial data, we can uniquely determine its time-evolution.

  • James Isenberg, "On Strong Cosmic Censorship". arXiv:1505.06390, 20 pages.
  • Mihalis Dafermos, Jonathan Luk, "The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon". arXiv:1710.01722, 217 pages.

Alternatives & Modifications to GR

  • Kirill Krasnov, Roberto Percacci, "Gravity and Unification: A review". arXiv:1712.03061, 84 pages; discusses many different actions describing gravity
  • Peter Peldan, "Actions for Gravity, with Generalizations: A Review". arXiv:gr-qc/9305011
  • H.F. Westman, T.G. Zlosnik, "An introduction to the physics of Cartan gravity". arXiv:1411.1679
  • Sarita Rosenstock, Thomas William Barrett, James Owen Weatherall, "On Einstein Algebras and Relativistic Spacetimes". arXiv:1506.00124, 19 pages.
  • Daniela Kunst, Tomáš Ledvinka, Georgios Lukes-Gerakopoulos, Jonathan Seyrich, "Comparing Hamiltonians of a spinning test particle for different tetrad fields". arXiv:1506.01473

Newton-Cartan Geometry

So, basically this is the geometric version of Newtonian gravity.

Note that when quantized, this is closely related to the Schrodinger-Newton equations. See also Quantum Newton Gravity.

  • Dieter Van den Bleeken, "Torsional Newton-Cartan gravity from the large c expansion of General Relativity". arXiv:1703.03459, 25 pages.
  • Michael Geracie, Kartik Prabhu, Matthew M. Roberts "Curved non-relativistic spacetimes, Newtonian gravitation and massive matter". arXiv:1503.02682
  • Christian Rueede, Norbert Straumann, "On Newton-Cartan Cosmology". arXiv:gr-qc/9604054
  • Xavier Bekaert, Kevin Morand, "Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view". arXiv:1412.8212, 79 pages.
  • Xavier Bekaert, Kevin Morand, "Connections and dynamical trajectories in generalised Newton-Cartan gravity II. An ambient perspective". arXiv:1505.03739, 71 pages.
  • Leo Rodriguez, James St.Germaine-Fuller, Sujeev Wickramasekara, "Newton-Cartan Gravity in Noninertial Reference Frames". arXiv:1412.8655, 16 pages
  • T.Dereli, S.Kocak, M.Limoncu, "Newton-Cartan connections with torsion". arXiv:gr-qc/0402116, 11 pages.
  • Roel Andringa, Eric Bergshoeff, Sudhakar Panda, M. de Roo, "Newtonian Gravity and the Bargmann Algebra". arXiv:1011.1145, 20 pages.
  • James Owen Weatherall, "Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?". arXiv:1411.5757, 22 pages, focuses more on what "equivalent theories" means in physics.
  • James Owen Weatherall, "What is a Singularity in Geometrized Newtonian Gravitation?". arXiv:1308.1722, 16 pages.

MOND

  • Dimitris M. Christodoulou, Demosthenes Kazanas, "Gauss's Law and the Source for Poisson's Equation in Modified Gravity with Varying G". arXiv:1901.02589, 6 pages

Spinors in Spacetime

  • Özgür Açık, "Field equations from Killing spinors". arXiv:1705.04685
  • Piotr Chruściel, Romain Gicquaud, "Bifurcating solutions of the Lichnerowicz equation". arXiv:1506.00101

BF Gravity

General relativity may be thought of as a constrained BF theory. A BF theory has an action that looks like

S = \int \tr(B\wedge F)

where B is a 2-form taking values in the adjoint representation of a fixed gauge group G, F = dA + A\wedge A is the field strength 2-form for the gauge field A (under the same gauge group G). Add constraints, and presto, you got GR...or something that resembles it.

Although we can have BF theories in any dimension, in 4 dimensions it is a topological field theory.

  • Mariano Celada, Diego González, Merced Montesinos, "BF gravity". arXiv:1610.02020, 54 pages.
  • Merced Montesinos, Mariano Celada, "Canonical analysis with no second-class constraints of BF gravity with Immirzi parameter". arXiv:1912.02832, 7 pages.
    • NOTE: Merced Montesinos and Mariano Celada seem to write quite a bit about BF gravity.

Kaluza-Klein Models

  • V H Satheesh Kumar, P K Suresh, "Gravitons in Kaluza-Klein Theory". Eprint arXiv:gr-qc/0605016, 12 pages

Composite Gravity

  • Christopher D. Carone, Joshua Erlich, Diana Vaman, "Composite gravity from a metric-independent theory of fermions". arXiv:1812.08201, 16 pages.

Geodesics

  • Eva Hackmann, "Geodesic equations and algebro-geometric methods". arXiv:1506.00804
  • Eva Hackmann, Claus Lämmerzahl, "Analytical solution methods for geodesic motion". arXiv:1506.00807
  • Eva Hackmann, Claus Lämmerzahl, "Analytical solutions for geodesics in black hole spacetimes". arXiv:1506.01572

Canonical Structure

We could think of GR as the "time evolution" of "spatial hypersurfaces". As long as we're not tied to one particular choice of time-slicing, we haven't violated diffeomorphism invariance. This is a deep field with heavy mathematics, so...be warned!

  • Maximilian Demmel, Andreas Nink, "On connections and geodesics in the space of metrics". arXiv:1506.03809

  • (?) Jürgen Struckmeier, "Generic Theory of Geometrodynamics from Noether's theorem for the Diff$(M)$ symmetry group". arXiv:1807.03000, 25 pages.

Einstein-Hilbert-Palatini Action

If we treat the connection as an independent variable from the metric, we end up with the Palatini formalism. The solution for the Palatini connection differs from the expected Levi-Civita connection, but is related by a projective transformation AND this is well-known "folklore" (see Dadhich and Pons for the sordid details). The usefulness of the Palatini formalism is that we may generalize it to different geometries quite easily (and ostensibly treat it completely algebraically) --- see Martins and Biezuner for their presentation.

  • Naresh Dadhich, Josep M. Pons, "On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection". arXiv:1010.0869, 18 pages
  • Yuri X. Martins, Rodney J. Biezuner, "Topological and Geometric Obstructions on Einstein--Hilbert--Palatini Theories". arXiv:1808.09249, 24 pages
  • Merced Montesinos, Ricardo Escobedo, Jorge Romero, Mariano Celada, "Canonical analysis involving first-class constraints only of the n-dimensional Palatini action". arXiv:1912.01019

Hamiltonian Formalism for Tetrad GR

NB: Deser and Isham's "Canonical vierbein form of general relativity" (1976) was the first paper, that I know of, which investigated the canonical structure of tetrads (triads?) in GR. There are, of course, other sources.

  • Karel Kuchar, "Canonical Quantum Gravity". arXiv:gr-qc/9304012, 35 pages.
  • Meriem Hadjer Lagraa, Mohammed Lagraa, Nabila Touhami, "On the Hamiltonian formalism of the tetrad-gravity". arXiv:1606.06918, 33 pages.
  • Luca Lusanna, "Canonical ADM Tetrad Gravity: from Metrological Inertial Gauge Variables to Dynamical Tidal Dirac observables". arXiv:1108.3224, 37 pages

Holst Action

Basically, as I understand it, tetrads + Palatini action = Holst action.

  • Alberto S. Cattaneo, Michele Schiavina, "The reduced phase space of Palatini-Cartan-Holst theory". arXiv:1707.05351, 31 pages.
  • Alberto S. Cattaneo, Michele Schiavina, "BV-BFV approach to General Relativity: Palatini-Cartan-Holst action". arXiv:1707.06328, 28 pages.

Hamiltonian Formalism for Linearized Gravity

I brush under this heading also Newtonian limits of spacetime splitting.

  • Oliver Lindblad Petersen, "On the Cauchy problem for the linearised Einstein equation". Eprint arXiv:1802.06028, 31 pages.
  • Maik Reddiger, "An Observer's View on Relativity: Space-Time Splitting and Newtonian Limit". Eprint arXiv:1802.04861, 109 pages

Mathematical Aspects

  • Olaf Müller, Miguel Sánchez, "Lorentzian manifolds isometrically embeddable in L^N". Trans. Amer. Math. Soc. 363 (2011), 5367-5379; arXiv:0812.4439. Proves it is equivalent for (i) a spacetime to be foliated into spatial hypersurfaces, and (ii) a spacetime admits an isometric embedding into an N-dimensional Minkowski spacetime (for some "large enough" N).

Derivations

  • Alberto S. Cattaneo, Michele Schiavina, "BV-BFV approach to General Relativity, Einstein-Hilbert action". arXiv:1509.05762, 16 pages.

Numerical Relativity

  • Helvi Witek, "Lecture Notes: Numerical Relativity in higher dimensional spacetimes". arXiv:1308.1686, 33 pages.
  • Eric Gourgoulhon, "3+1 Formalism and Bases of Numerical Relativity". arXiv:gr-qc/0703035, 220 pages.

Regge Calculus

  • Seth K. Asante, Bianca Dittrich, Hal M. Haggard, "The Degrees of Freedom of Area Regge Calculus: Dynamics, Non-metricity, and Broken Diffeomorphisms". arXiv:1802.09551, 31 pages
  • H.W. Hamber, R.M Williams, "Gauge Invariance in Simplicial Gravity". Nucl.Phys. B487 (1997) 345-408, arXiv:hep-th/9607153, 68 pages.
  • Philipp A. Hoehn "Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves". arXiv:1411.5672, 26+13 pages
  • Barak Shoshany, "At the Corner of Space and Time". arXiv:1912.02922, 162 pages. PhD Thesis.

Restrictions on underlying Manifold

Spacetime is a manifold, but it has to allow a Lorentzian signature. Further, we appear to have, e.g., chiral fermions...which requires additional structure on the manifold.

  • A. Carlini, J. Greensite. "Why is Spacetime Lorentzian?". Phys.Rev. D49 (1994) 866-878. Eprint arXiv:gr-qc/9308012, 26 pages.
  • Deloshan Nawarajan, Matt Visser, "Global properties of physically interesting Lorentzian spacetimes". Eprint arXiv:1601.03355, 19 pages. (Turns out spacetime ought to be parallelizable, and there's an almost-unavoidable globally defined "almost complex structure".)

Wick Rotations

It is folklore that Wick rotations...well, there are subtle problems with doing it in general relativity as cavalier as we do it in quantum field theory. We can transform Lorentzian manifolds into Euclidean manifolds just fine, but the inverse transformation is not well-defined: it's a one-way trip to Euclidean spacetime, with no return ticket.

  • Alessio Baldazzi, Roberto Percacci, Vedran Skrinjar, "Quantum fields without Wick rotation". arXiv:1901.01891, 18 pages.
  • Matt Visser, "How to Wick rotate generic curved spacetime". arXiv:1702.05572, 11 pages.
  • Chien-Hao Liu, "Remarks on the Geometry of Wick Rotation in QFT and its Localization on Manifolds". arXiv:hep-th/9707196, 24 pages.

Coupled to various matter fields

  • Burkhard Kleihaus, Jutta Kunz, "Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: I.Regular Solutions". arXiv:gr-qc/9707045

Instantons

Generically, an "instanton" is a static, stable solution to the Euclidean field equations such that the solution has finite energy. It's also a "packet" in the sense that at infinity, the solution is pure gauge. Gravitational instantons are defined analogously, they are asymptotically Euclidean solutions to the Wick rotated field equations with finite action. For more on Yang-Mills instantons, Rubakov's Classical Theory of Gauge Fields is a great reference.

  • Don Page, "Some Gravitational Instantons". arXiv:0912.4922
  • G. W. Gibbons and S. W. Hawking, "Classification of gravitational instanton symmetries". Comm. Math. Phys. 66 no.3 (1979), 291-310. Eprint

Time-Independent Spacetimes

  • Robert Beig, Bernd G. Schmidt, "Time-Independent Gravitational Fields". arXiv:gr-qc/0005047, 47 pages, review article.
  • Joseph Katz, Donald Lynden-Bell, Jiri Bicak, "Gravitational energy in stationary spacetimes". arXiv:gr-qc/0610052, 24 pages, published in Classical and Quantum Gravity.

Empirical Aspects

Gravitational Waves Constraints on Extra-Dimensions

  • Kris Pardo, Maya Fishbach, Daniel E. Holz, David N. Spergel, "Limits on the number of spacetime dimensions from GW170817". Eprint arXiv:1801.08160

Quantum Gravity

Semiclassical Quantum Gravity

Quantum Field Theory in Curved Spacetime

There seems to be two types of texts in this field: (i) the more "Euler-esque" approaches, (ii) those based on "Axiomatic Field Theory". The former I call "QFT in curved space", the latter I call "Axiomatic QFT (or Constructive QFT) on arbitrary manifolds". Needless to say, we need to work out calculations in position-space, and -- in the words of a friend -- "it's really disgusting" (but I find it kinda beautiful).

  • L.H. Ford, "Quantum Field Theory in Curved Spacetime". arXiv:gr-qc/9707062
  • Christopher J. Fewster, "On the spin-statistics connection in curved spacetimes". arXiv:1503.05797
  • Marco Benini, Claudio Dappiaggi, "Models of free quantum field theories on curved backgrounds". arXiv:1505.04298

For the more historic "Euler-esque" approaches, see:

  • Hanno Gottschalk, Daniel Siemssen, "The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System". arXiv:1809.03812, 33 pages
  • Eanna Flanagan, Robert Wald, "Does backreaction enforce the averaged null energy condition in semiclassical gravity?". arXiv:gr-qc/9602052, 54 pages. (Discusses deviations from full quantum gravity in Sect. II.B.)

Dirac Equation

  • Peter Collas, David Klein, "The Dirac equation in general relativity, a guide for calculations". arXiv:1809.02764, 59 pages

Scattering in Curved Spacetime

  • Antoine Folacci, Mohamed Ould El Hadj, "Regge pole description of scattering of scalar and electromagnetic waves by a Schwarzschild black hole". arXiv:1901.03965, 14 pages

Algebraic QFT in Curved Spacetime

  • Christopher J. Fewster, Rainer Verch, "Algebraic quantum field theory in curved spacetimes". arXiv:1504.00586, 62 pages.

Dependence on choice of Time-Slices

So, the functional Schrodinger picture requires great care when working with different time-slicing schemes, and even the slightest bit of sloppiness can cause problems. Torre and Varadarajan's arXiv:hep-th/9811222 investigates what happens when we consider the time-evolution in Minkowski spacetime between two space-like Cauchy surfaces, but with two different time-slicings. It appears that only in (1+1)-spacetime dimensions there is no problem (which was investigated earlier in arXiv:hep-th/9707221), but for d>2-spacetime dimensions...there is a problem. Stoyanovsky seems to have a way around it, but the approach seems coordinate-dependent in a bad way (arguably the Schrodinger picture is "coordinate dependent", but when changing coordinates the results should transform appropriately --- Stoyanovsky's solution does not appear to "transform appropriately", hence it is "badly coordinate dependent").

Born's Rule also has some subtleties. I need to read the Lienert and Tumulka paper a bit more, but I am immediately distressed with their citations to Wikipedia as opposed to...any actual book or paper or preprint.

  • Matthias Lienert, Roderich Tumulka, "Born's Rule for Arbitrary Cauchy Surfaces". arXiv:1706.07074
  • A. V. Stoyanovsky, "Quantization on space-like surfaces". arXiv:0909.4918
  • C. G. Torre, M. Varadarajan, "Quantum Fields at Any Time". arXiv:hep-th/9707221, 42 pages
  • C. G. Torre, M. Varadarajan, "Functional Evolution of Free Quantum Fields". arXiv:hep-th/9811222, 21 pages.

Nonlocality

  • Xavier Calmet, Djuna Croon, Christopher Fritz, "Non-locality in Quantum Field Theory due to General Relativity". arXiv:1505.04517

Pair Production

  • Ram Brustein, A.J.M. Medved, "Constraints on the quantum state of pairs produced by semiclassical black holes". arXiv:1503.05351
  • L. P. Pitaevskiî and Ya. B. Zeldoviĉ, "On the possibility of the creation of particles by a classical gravitational field". Comm. Math. Phys. 23 no.3 (1971) 185-188, eprint.

Renormalization of the Stress-Energy Tensor

  • Christopher J. Fewster, "Energy Inequalities in Quantum Field Theory". arXiv:math-ph/0501073
  • F. Finelli, G. Marozzi, G. P. Vacca, G. Venturi, "Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time". arXiv:gr-qc/0407101; Finelli, et al., have written other interesting works on the arXiv
  • Aitor Landete, Jose Navarro-Salas, Francisco Torrenti, "Adiabatic regularization for spin-1/2 fields". arXiv:1305.7374
  • Tommi Markkanen, Anders Tranberg, "A Simple Method for One-Loop Renormalization in Curved Space-Time". arXiv:1303.0180
  • Thomas-Paul Hack, Valter Moretti, "On the Stress-Energy Tensor of Quantum Fields in Curved Spacetimes - Comparison of Different Regularization Schemes and Symmetry of the Hadamard/Seeley-DeWitt Coefficients". J.Phys. A: Math.Theor. 45 (2012) 374019. Eprint arXiv:1202.5107.
  • Yu. V. Pavlov, "The n-wave procedure and dimensional regularization for the scalar field in a homogeneous isotropic space". arXiv:gr-qc/0403008
  • Robert T. Thompson, José P. S. Lemos, "DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions". arXiv:0811.3962
  • Robert T. Thompson, José P.S. Lemos, "DeWitt-Schwinger Renormalization of 〈φ2⟩ in d Dimensions". arXiv:1011.2598

Adiabatic Regularization

  • Aitor Landete, Jose Navarro-Salas, Francisco Torrenti, "Adiabatic regularization for spin-1/2 fields". arXiv:1305.7374
  • Wolfgang Junker, "Adiabatic Vacua and Hadamard States for Scalar Quantum Fields on Curved Spacetime". arXiv:hep-th/9507097, 72 pages
  • Wolfgang Junker, Elmar Schrohe, "Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties". arXiv:math-ph/0109010
  • Joachim Lindig, "Not all adiabatic vacua are physical states". arXiv:hep-th/9808133, 13 pages
  • Adrian del Rio, Jose Navarro-Salas, "On the equivalence of Adiabatic and DeWitt-Schwinger renormalization schemes". arXiv:1412.7570

Unruh Effect

Basically, consider in Minkowski space a detector coupled to a scalar field. Suppose there is no source for the scalar field, and in an inertial frame the detector registers 0 particles. When the detector experiences uniform acceleration, it begins registering particles. This "thermal bath" of particles is the Unruh effect.

(Well, the Unruh effect is more general than this, but it's a good "particular example" of the more general phenomena.)

If we ask "Well, which one is right?", then as with most paradoxes the answer is "Both".

  • Lee Hodgkinson, "Particle detectors in curved spacetime quantum field theory". arXiv:1309.7281 PhD Thesis, 232 pages.
  • M. Socolovsky, "Rindler Space and Unruh Effect". arXiv:1304.2833
  • Daniel Hümmer, Eduardo Martin-Martinez, Achim Kempf, "Renormalized Unruh-DeWitt Particle Detector Models for Boson and Fermion Fields". arXiv:1506.02046
  • Jorma Louko, Alejandro Satz, "Transition rate of the Unruh-DeWitt detector in curved spacetime". arXiv:0710.5671
  • Luis C. B. Crispino, Atsushi Higuchi, George E. A. Matsas, "The Unruh effect and its applications". arXiv:0710.5373, 53 pages. Good review.

Energy Inequalities

  • Christopher J. Fewster, "Lectures on quantum energy inequalities". arXiv:1208.5399, 50 pages.

Black Hole Thermodynamics

  • Nikolaos Kalogeropoulos, "Embolic aspects of black hole entropy". arXiv:1712.02978, 9 pages; discusses mescoscopic aspects of BH entroy.

Effective Field Theory

  • C.P. Burgess, "Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory". arXiv:gr-qc/0311082, 56 pages.
  • John F. Donoghue, Barry R. Holstein, "Low Energy Theorems of Quantum Gravity from Effective Field Theory". arXiv:1506.00946, 35 pages.

Asymptotic Safety

Using a scale-dependent effective action, the functional renormalization group flow is computed for a truncated action (usually of the form $L_{EH} + (bonus parts as a polynomial in Ricci tensor and metric)$). Certain statements can be made about quantum gravity, e.g., at "sufficiently small scales" spacetime (in some appropriate sense) "appears 2-dimensional".

  • Frank Saueressig, Giulia Gubitosi, Chris Ripken, "Scales and hierachies in asymptotically safe quantum gravity: a review". arXiv:1901.01731, 18 pages.

Gravitons

  • Johannes Noller, James H.C. Scargill, Pedro G. Ferreira, "Interacting spin-2 fields in the Stueckelberg picture". arXiv:1311.7009
  • Norbert Straumann, "Reflections on Gravity". arXiv:astro-ph/0006423

Graviton Scattering

  • J. F. Donoghue, T. Torma, "Infrared behavior of graviton-graviton scattering". arXiv:hep-th/9901156, 12 pages

Path Integral Approach

  • J. David Brown, James W. York "The Microcanonical Functional Integral. I. The Gravitational Field". arXiv:gr-qc/9209014

Causal Dynamical Triangulations

The path integral approach...blows up, so we do what we always do: use a lattice! There are two ways to do this: causal dynamical triangulations, and quantum Regge calculus. The former works with a fixed tetrahedron, but a variable number of them. The quantum Regge calculus consists of varying the edge lengths. It looks like CDT is the "right" approach.

  • J. Ambjorn, A. Goerlich, J. Jurkiewicz, H. Zhang, "The microscopic structure of 2D CDT coupled to matter". arXiv:1503.01636
  • J. Ambjorn, A. Goerlich, J. Jurkiewicz, R. Loll, "Wilson loops in CDT quantum gravity". arXiv:1504.01065, 30 pages
  • J. Ambjorn, Y. Watabiki, "A model for emergence of space and time". arXiv:1505.04353

Euclidean Dynamical Triangulations

This actually pre-dates CDT, but never caught on because it resulted in polymer universes.

  • Tobias Rindlisbacher, Philippe de Forcrand, "Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order?". arXiv:1503.03706

Discrete Approaches to Gravity

  • Benjamin Bahr, Bianca Dittrich, "Improved and Perfect Actions in Discrete Gravity". arXiv:0907.4323
  • Bianca Dittrich, Wojciech Kaminski, Sebastian Steinhaus "Discretization independence implies non-locality in 4D discrete quantum gravity". arXiv:1404.5288, 18 pages.

Canonical Quantization Schemes

  • I.V. Kanatchikov, "On precanonical quantization of gravity". arXiv:1407.3101

Wheeler-DeWitt Equation

Loop Quantum Gravity

Originally, this began from a quantization using a different choice of variables. It has since blossomed into a unique field that seems distinct from the previous canonical quantization schemes, probably due to the (i) Loop quantization scheme, (ii) use of spin foams.

Kinematical Phase Space

If we have a system with constraints, one way to approach quantizing it is to treat the constraints as operators acting on the "kinematical Hilbert space". The kernel of the constraint operators is the "physical Hilbert space".

  • Kristina Giesel, "The kinematical Setup of Quantum Geometry: A Brief Review". arXiv:1707.03059, 46 pages.

Weak Coupling Limit

  • Lee Smolin, "The G_Newton --> 0 Limit of Euclidean Quantum Gravity". Class.Quant.Grav. 9 (1992) 883-894. Eprint arXiv:hep-th/9202076
  • Madhavan Varadarajan, "The constraint algebra in Smolins' G→0 limit of 4d Euclidean Gravity". Eprint arXiv:1802.07033, 123 pages

Spin Networks

  • Jerzy Lewandowski, Andrzej Okolow, Hanno Sahlmann, Thomas Thiemann, "Uniqueness of diffeomorphism invariant states on holonomy-flux algebras". arXiv:gr-qc/0504147. Basically a uniqueness theorem saying spin foams all describe "the same" theory of quantum gravity. The assumptions for the theorem appear to be (i) irreducibility, (ii) the requirement that spatial diffeomorphisms act as automorphisms and leave the vacuum invariant, and (iii) the requirement that fluxes exist either as operators or as a weakly continuous operator family of exponentiated fluxes.
  • Bianca Dittrich, Marc Geiller, "Flux formulation of loop quantum gravity: Classical framework". Class. Quantum Grav. 32 (2015) 135016. Eprint arXiv:1412.3752; an example of a spin network algebra that violates one of the assumptions of the LOST theorem, but in some sense describes an algebra "dual" to the usual Ashtekar-Lewandowski-Isham algebra.

Classical Limit

  • Bianca Dittrich, "The continuum limit of loop quantum gravity - a framework for solving the theory". arXiv:1409.1450
  • Bianca Dittrich, Marc Geiller, "Flux formulation of loop quantum gravity: Classical framework". arXiv:1412.3752

...and Noncommutative Geometry

Johannes Aastrup and Jesper M. Grimstrup appear to be examining Ashtekar variables in the noncommutative geometry formalism, and it looks fascinating. When time allows, I should read this further.

  • Johannes Aastrup, Jesper M. Grimstrup, "Quantum Holonomy Theory". arXiv:1504.07100

2+1-Dimensional Gravity

  • Alejandro Corichi, Irais Rubalcava-Garcia, "Energy in first order 2+1 gravity". arXiv:1503.03030
  • Simone Giombi, Alexander Maloney, Xi Yin, "One-loop Partition Functions of 3D Gravity". arXiv:0804.1773

Black Hole Entropy

  • Yasunori Nomura, Sean J. Weinberg, "The Entropy of a Vacuum: What Does the Covariant Entropy Count?". arXiv:1310.7564
  • Alioscia Hamma, Ling-Yan Hung, Antonino Marciano, Mingyi Zhang, "Area Law from Loop Quantum Gravity". arXiv:1506.01623

Quantum Newton Gravity

  • Joy Christian, "Exactly Soluble Sector of Quantum Gravity". arXiv:gr-qc/9701013, 83 pages
  • Maciej Dunajski, James Gundry, "Non-relativistic twistor theory and Newton--Cartan geometry". arXiv:1502.03034
  • Eric Bergshoeff, Jan Rosseel, Thomas Zojer, "Newton-Cartan (super)gravity as a non-relativistic limit". arXiv:1505.02095, 28 pages

Schrodinger-Newton Equation

  • C Duval, Serge Lazzarini, "On the Schrödinger-Newton equation and its symmetries: a geometric view". arXiv:1504.05042, 28 pp.
  • C. C. Gan, C. M. Savage, S. Scully, "Experimental semiclassical gravity" arXiv:1512.04183, 7 pages. Discusses experimental aspects of many-body Schrodinger-Newton problem.

Problem of Time

  • W.G. Unruh and R.M. Wald, "Time and the interpretation of canonical quantum gravity." Phys. Rev. D 40 (1989) 2598--2614, eprint, proved that if time is treated as a quantum observable, then the Hamiltonian becomes unbounded from below.
  • Christopher Isham, "Canonical Quantum Gravity and the Problem of Time". arXiv:gr-qc/9210011, 125 pages. Authoritative review, still today one of the best.
  • Sandra Ranković, Yeong-Cherng Liang, Renato Renner, "Quantum clocks and their synchronisation - the Alternate Ticks Game". arXiv:1506.01373

Minisuperspace and Midisuperspace Models

We can use symmetry to simplify many models in quantum gravity. When the symmetry kills boils everything down to a finite number of parameters, we have a "minisuperspace model". If we have a finite number of functions, we have a "midisuperspace model".

  • J. Fernando Barbero G. and Eduardo J. S. Villaseñor, "Quantization of Midisuperspace Models". Living Rev. Relativity 13 (2010), 6 - Eprint
  • C. G. Torre, "Midi-superspace Models of Canonical Quantum Gravity". arXiv:gr-qc/9806122

Miscellaneous

  • Rafael A. Araya-Gochez, "On the Geometry of Spacetime I: baby steps in quantum ring theory". arXiv:1411.1728
  • Bob Holdom, Jing Ren, "A QCD analogy for quantum gravity". arXiv:1512.05305
Raw
math.md

Mathematics

Classical Analysis and Differential Equations

  • Omran Kouba, "Lecture Notes, Bernoulli Polynomials and Applications". arXiv:1309.7560, 48 pages.

Number Systems

Partial Differential Equations

  • Robert Geroch, "Partial Differential Equations of Physics". arXiv:gr-qc/9602055
  • Per Kristen Jakobsen, "An Introduction to Partial Differential Equations". arXiv:1901.03022, 225 pages.

Group Theory

  • Tevian Dray, Corinne A. Manogue, Robert A. Wilson "A Symplectic Representation of E7". arXiv:1311.0341, 12 pages
  • John F. Duncan, "Arithmetic groups and the affine E8 Dynkin diagram". arXiv:0810.1465, 33 pages.
  • Ching Hung Lam, Hiromichi Yamada, Hiroshi Yamauchi, "Vertex operator algebras, extended E_8 diagram, and McKay's observation on the Monster simple group". arXiv:math/0403010
  • V. D. Mazurov, E. I. Khukhro, "The Kourovka Notebook. No. 18". arXiv:1401.0300
  • Ichiro Yokota, "Exceptional Lie groups". arXiv:0902.0431, 204 pages.

Moonshine

  • Vassilis Anagiannis, Miranda C. N. Cheng, "TASI Lectures on Moonshine". arXiv:1807.00723, 78 pages.
  • John F. R. Duncan, Michael J. Griffin, Ken Ono, "Moonshine". arXiv:1411.6571, 67 pages.
  • Robert L. Griess Jr., Ching Hung Lam, "A moonshine path from E8 to the monster". arXiv:0910.2057, 42 pages
  • Robert L. Griess Jr., Ching Hung lam, "Moonshine paths for 3A and 6A nodes of the extended E8-diagram". arXiv:1205.6017, 40 pages
  • Theo Johnson-Freyd, "The Moonshine Anomaly". arXiv:1707.08388, 16 pages.
  • Hiroki Shimakura, "An E8-approach to the moonshine vertex operator algebra". arXiv:1009.4752, 25 pages

Finite Groups

  • Nick Gill, Pablo Spiga, "Binary permutation groups: alternating and classical groups". arXiv:1610.01792, 43 pages.
  • Nick Gill, Francesca Dalla Volta, Pablo Spiga, "Cherlin's conjecture for sporadic simple groups". arXiv:1705.05150, 11 pages. The paper on binary permutation groups has useful background terminology needed to understand this paper.
  • Ilya Gorshkov, Ivan Kaygorodov, Andrei Kukharev, Aleksei Shlepkin, "On Thompson's conjecture for finite simple exceptional groups of Lie type". arXiv:1707.01963, 6 pages
  • Sanhan Khasraw, Justin McInroy, Sergey Shpectorov, "Enumerating 3-generated axial algebras of Monster type". arXiv:1809.10657, 26 pages
  • Robert A Wilson, "There is no Sz(8) in the Monster". arXiv:1508.04996, 9 pages

Combinatorics

  • Darij Grinberg, Victor Reiner, "Hopf Algebras in Combinatorics". arXiv:1409.8356, 186 pages.
  • Dániel T. Soukup, Lajos Soukup, "Infinite combinatorics plain and simple". arXiv:1705.06195, 29 pages.

Differential Geometry

  • Manuel Gutiérrez, Olaf Müller, "Compact Lorentzian holonomy". Eprint arXiv:1502.05289.
    • Proves: If a Lorentzian manifold M has its holonomy group Hol(M) have compact closure, then M is "locally isometric" to ℝ × N. Not too surprising that locally M looks like (time)×(space)...
  • Liviu Popescu, "Geometrical structures on the cotangent bundle". arXiv:1410.1118
  • Toshikazu Miyashita, "Realization of globally exceptional Riemannian $4$-symmetric space $E_8/(E_8)^{σ'_{4}}$". arXiv:1506.03575
  • Zafar Ahsan, Musavvir Ali, Sirajuddin, "On a Curvature Tensor for the Spacetime of General Relativity". arXiv:1506.03476

Lorentzian Geometries

  • Abdelghani Zeghib, "Geometry of warped products". arXiv:1107.0411, 25 pages.

In Infinite Dimensions

Finite Geometry

Rings and Things

  • Alonso Castillo-Ramirez, Justin McInroy, Felix Rehren, "Code algebras, axial algebras and VOAs". arXiv:1707.07992, 30 pages
  • Miodrag C. Iovanov, Zachary Mesyan, Manuel L. Reyes, "Infinite-dimensional diagonalization and semisimplicity". Eprint arXiv:1502.05184

Number Theory

  • Minhyong Kim, "Arithmetic Gauge Theory: A Brief Introduction". Eprint arXiv:1712.07602

Logic

Automated Theorem Provers

  • Thomas C. Hales, "Developments in Formal Proofs". Eprint
  • Martin Hoffman, "Syntax and Semantics of Dependent Types". Eprint
  • Lawrence Paulson, "Computational Logic: Its Origins and Applications". arXiv:1712.04375

Lambda Calculus

Typed lambda calculus turns out to be a critical component of most automated theorem provers.

  • Peter Selinger, "Lecture notes on the lambda calculus". arXiv:0804.3434, 120 pages.

Type Theory

Cubical Type Theory

Mortberg motivates Cubical Type Theory:

Goal: provide a computational justification for notions from HomotopyType Theory and Univalent Foundations, in particular the univalenceaxiom and higher inductive types.

Specifically, design a type theory with good properties (normalization, decidability of type checking, etc.) where the univalence axiom computesand which has support for higher inductive types.

  • Cyril Cohen, Thierry Coquand, Simon Huber, Anders Mörtberg, Cubical Type Theory: a constructive interpretation of the univalence axiom
  • Cyril Cohen, Thierry Coquand, Simon Huber, Anders Mörtberg, "Cubical Type Theory: a constructive interpretation of the univalence axiom". arXiv:1611.02108, 34 pages
  • Evan Cavallo, Robert Harper, "Parametric Cubical Type Theory". arXiv:1901.00489, 47 pages.

Topology

Algebraic Topology

Cohomology

  • Matvei Libine, "Lecture Notes on Equivariant Cohomology". arXiv:0709.3615, 72 pages.
Raw
meta.md

Principles

  • Isolate papers by field, then by subject.
  • Papers are organized by author names, then by year.
  • Try to include the number of pages, and a link to a (legally) free version.
Raw
qft.md

Particle physics and Quantum Field Theory papers, including stuff related to GUTs and the group theory of the standard model.

Quantum Field Theory

Methods of Quantization

There are three pictures: the Heisenberg picture, which is usually taught as "the canonical approach"; the functional Schrodinger picture, which is rarely discussed; and the Feynman path integral approach.

Functional Schrodinger Picture

  • Alejandro Corichi, Jeronimo Cortez, Hernando Quevedo "On the Relation Between Fock and Schroedinger Representations for a Scalar Field". arXiv:hep-th/0202070
  • -----, -----, -----, "On the Schroedinger Representation for a Scalar Field on Curved Spacetime". arXiv:gr-qc/0207088
  • I.V. Kanatchikov, "On the precanonical structure of the Schrödinger wave functional". arXiv:1312.4518
  • -----, "Precanonical Quantization and the Schrödinger Wave Functional Revisited". arXiv:1112.5801
  • Chul Koo Kim, Sang Koo You, "The Functional Schrödinger Picture Approach to Many-Particle Systems". arXiv:cond-mat/0212557
  • Paul Mansfield, Marcos Sampaio, "Yang-Mills beta-function from a large-distance expansion of the Schroedinger functional". arXiv:hep-th/9807163

Path Integral Approach

  • Kimichika Fukushima, Hikaru Sato, "Example of an explicit function for confining classical Yang-Mills fields with quantum fluctuations in the path integral scheme". arXiv:1402.0450
  • Timothy Nguyen, "The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment". arXiv:1505.04809, 26 pages.
  • Stefan Weinzierl, "Introduction to Feynman Integrals". arXiv:1005.1855, 43 pages

Semiclassical Techniques

  • Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, "Semiclassical quantization of classical field theories". arXiv:1311.2490, 36 pages.

Families of Fields

Really, QFT studies three families of fields: scalar (spin-0), Dirac (spin-1/2), and gauge bosons (spin-1, or "vector fields"). Higher spin fields (e.g., the Rarita-Schwinger (spin-3/2) field) are usually non-renormalizable or have some other problems.

(Spin-0) Scalar Field

  • Nik Weaver, "Operator algebras associated with the Klein-Gordon position representation in relativistic quantum mechanics". arXiv:math/0209079, 28 pages

(Spin-1/2) Dirac Field

  • C. J. Quimbay, Y. F. Pérez, R. A. Hernandez, "Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions". arXiv:1201.3389

(Spin-1) Vector Bosons

QED

  • Miguel Campiglia, Alok Laddha, "Asymptotic symmetries of QED and Weinberg's soft photon theorem". arXiv:1505.05346, 16 pages

Yang-Mills Theory

  • Alexander D. Popov, "Loop groups in Yang-Mills theory". arXiv:1505.06634, 7 pages.
  • James Owen Weatherall, "Fiber Bundles, Yang-Mills Theory, and General Relativity". arXiv:1411.3281, 54 pages; discusses Yang-Mills theory "geometrically", in analogy to classical General Relativity.

(Spin-3/2) Rarita-Schwinger Field

(Spin-2) Graviton

There's actually a "uniqueness theorem" stating, basically, spin-2 fields couple to everything in exactly the same way, up to some proportionality constant. This is the paper of Boulanger, Damour, Gualtieri, and Henneaux, "Inconsistency of interacting, multi-graviton theories" (2001).

  • Nicolas Boulanger, Thibault Damour, Leonardo Gualtieri, Marc Henneaux, "Inconsistency of interacting, multi-graviton theories". Nucl.Phys. B597 (2001) 127-171 doi:10.1016/S0550-3213(00)00718-5 arXiv:hep-th/0007220, 44+1 pages.
  • Nicolas Boulanger, Thibault Damour, Leonardo Gualtieri, Marc Henneaux, "No consistent cross-interactions for a collection of massless spin-2 fields". arXiv:hep-th/0009109, 12+1 pages.

Nonlinear Sigma Models

  • Noriaki Ikeda, "Lectures on AKSZ Sigma Models for Physicists". arXiv:1204.3714, 97 pages.
  • Timothy Nguyen, "Quantization of the Nonlinear Sigma Model Revisited". arXiv:1408.4466, 51 pages.

Feynman Diagrams

These are usually covered too briefly in most textbooks, probably because to understand them adequately you need to see someone draw such a diagram, then walk through "translating" a diagram into an integral.

  • Michael Polyak, "Feynman diagrams for pedestrians and mathematicians". arXiv:math/0406251, 28 pages.

Symmetries in QFT

Wigner's Theorem

Group Theory

  • Andrew Douglas, Joe Repka, "The GraviGUT Algebra Is not a Subalgebra of E8, but E8 Does Contain an Extended GraviGUT Algebra". arXiv:1305.6946

Renormalization, Renormalization "Group"

The basic scheme:

  • Step 0: Write down your Lagrangian
  • Step 1: Do dimensional regularization
  • Step 2: Replace "bare" constants like mass m_{bare} with "renormalized" constants m related by m = Z_{m}m_{bare}, then
  • Step 3: Make certain the propagators and vertex contributions "work out".

An example of this is worked out in this handout.

Remark. This is all from memory, I need to review the details a bit more. But that's the gist of the renormalization game, introduce counter-terms, etc. This will give us also the renormalization group flow, which is used to determine if the theory is "asymptotically free" or "asymptotically safe". (End of Remark)

  • Abdelmalek Abdesselam, "QFT, RG, and all that, for mathematicians, in eleven pages". arXiv:1311.4897, 11 pages.
  • Kevin Costello, Renormalization and Effective Field Theory. AMS publishers, 2011.
  • Alessandra Frabetti, "Renormalization Hopf algebras and combinatorial groups". arXiv:0805.4385, 37 pages.
  • Arnold Neumaier, Renormalization Without Infinities.

In Curved Spacetime

Puzzle. Is dimensional regularization "coordinate independent" (in the sense, can we use it in curved spacetime)? Is there some generic criteria we can use to determine if a regularization scheme is "coordinate independent"? Which ones are "coordinate independent"? (End of Puzzle)

I have seen Shapiro et al. argue only the MS-bar renormalization scheme works in curved spacetime, as the other schemes fail. But I do not adequately understand the details. It is asserted (quite boldly) in Renormalization Group in Curved Space and the Problem of Conformal Anomaly that:

An alternative way is to use some more sophisticated scheme of renormalization, which would not be universal one as the MS-based RG is, but which should be designed especially for the given application. Unfortunately, there is no covariant renormalization scheme except the MS one. Furthermore, the known renormalization schemes (e.g. the momentum subtraction scheme) of renormalization are not really appropriate for the use in the gravitational framework. Still the momentum subtraction scheme enables one to extract some relevant information, [...].

Apparently they are contained in the following resources:

  • I.L. Buchbinder, S.D. Odintsov and I.L. Shapiro, Effective Action in Quantum Gravity. IOP Publishing, Bristol, 1992.

Asymptotic Safety

  • Andrew D. Bond, Daniel F. Litim, "Theorems for Asymptotic Safety of Gauge Theories". arXiv:1608.00519
  • R. Percacci, "Asymptotic Safety". arXiv:0709.3851, 25 pages.
  • R. Percacci, "A short introduction to asymptotic safety". arXiv:1110.6389, 18 pages, a good general introduction.

Case Studies ("Examples")

  • M. Fabbrichesi, R. Percacci, A. Tonero, O. Zanusso, "Asymptotic safety and the gauged SU(N) nonlinear sigma-model". arXiv:1010.0912, 11 pages.
  • Daniel F. Litim, Francesco Sannino, "Asymptotic safety guaranteed". arXiv:1406.2337, 31 pages.
  • Andrew D. Bond, Daniel F. Litim, "More asymptotic safety guaranteed". arXiv:1707.04217, 62 pages.

Assorted Lecture Notes

  • Luis Alvarez-Gaume, Miguel A. Vazquez-Mozo, "Introductory Lectures on Quantum Field Theory". arXiv:hep-th/0510040, 113 pages.
  • V. Parameswaran Nair, Quantum Field Theory: A Modern Perspective. Springer-Verlag.
  • Various introductory texts are discussed on Physics.SE

Quantization of Constrained Systems

  • Bianca Dittrich, Philipp A. Hoehn, Tim A. Koslowski, Mike I. Nelson, "Chaos, Dirac observables and constraint quantization". arXiv:1508.01947, 48 pages.

Quantizing Gauge Systems

  • N. Reshetikhin, "Lectures on quantization of gauge systems". arXiv:1008.1411, 63 pages.

Conformal and Topological Field Theory

Conformal Field Theory

Topological Field Theory

  • Jian Qiu, "Lecture Notes on Topological Field Theory". arXiv:1201.5550, 64 pages - nice discussion of Chern-Simons as a TQFT.
  • George Thompson, "1992 Trieste Lectures on Topological Gauge Theory and Yang-Mills Theory". arXiv:hep-th/9305120, 70 pages. Discusses Yang-Mills on Riemann surfaces.

Chern-Simons Models

BF Theories

  • John C. Baez, "4-Dimensional BF Theory as a Topological Quantum Field Theory". arXiv:q-alg/9507006, 15 pages.
  • Aberto S. Cattaneo, Paolo Cotta-Ramusino, Juerg Froehlich, Maurizio Martellini, "Topological BF Theories in 3 and 4 Dimensions". arXiv:hep-th/9505027, 25 pages.
  • Pavel Mnev, "Discrete BF theory". arXiv:0809.1160, 204 pages.

Anomalies

Particle Physics

Froissart Bound

For elastic processes, the total cross sections grows like log(log(s/s0)) for some constant s0.

Complex Angular Momentum, S-Matrix, Regge Poles

  • Alessandro Bottino, "A retrospective look at Regge poles". arXiv:1807.02456
  • Vittorio Del Duca, Lorenzo Magnea, "The long road from Regge poles to the LHC". arXiv:1812.05829, 21 pages

Heavy Quark Physics

Note Mark Wise wrote the book on this subject...

Effective Field Theory

  • Clifford Cheung, Karol Kampf, Jiri Novotny, Chia-Hsien Shen, Jaroslav Trnka, "A Periodic Table of Effective Field Theories". arXiv:1611.03137
  • Henriette Elvang, Callum R. T. Jones, Stephen G. Naculich, "Soft Photon and Graviton Theorems in Effective Field Theory". arXiv:1611.07534, 6 pages.
  • Andrew J. Larkoski, Duff Neill, Iain W. Stewart, "Soft Theorems from Effective Field Theory". arXiv:1412.3108
  • J.M. Campbell, J.W. Huston, W.J. Stirling, "Hard Interactions of Quarks and Gluons: a Primer for LHC Physics". arXiv:hep-ph/0611148, 118 pages.

Composite Higgs Boson

  • Giuliano Panico, Andrea Wulzer, "The Composite Nambu-Goldstone Higgs". arXiv:1506.01961, 325 pages --- a monograph in preparation for Springer-Verlag.

Standard Model

  • Scott Willenbrock, "Symmetries of the Standard Model". arXiv:hep-ph/0410370, 31 pages.
  • J. C. Montero, V. Pleitez, "Custodial Symmetry and Extensions of the Standard Model". arXiv:hep-ph/0607144, 12 pages.
  • Paul Langacker, "Structure of the Standard Model". arXiv:hep-ph/0304186, 22 pages.
  • Jean Iliopoulos, "Introduction to the Standard Model of the Electro-Weak Interactions". arXiv:1305.6779, 44 pages. Discusses (i) A brief summary of the phenomenology of the electromagnetic and the weak interactions; (ii) Gauge theories, Abelian and non-Abelian; (iii) Spontaneous symmetry breaking; (iv) The step-by-step construction of the Standard Model; (v) The Standard Model and experiment.
  • Brian Henning, Xiaochuan Lu, Hitoshi Murayama, "How to use the Standard Model effective field theory" arXiv:1412.1837, 94 pages.

Phenomenology

Scattering Amplitudes

  • Detlev Buchholz, Stephen J. Summers, "Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools". arXiv:math-ph/0509047, 14 pages
  • Clifford Cheung, "TASI Lectures on Scattering Amplitudes". arXiv:1708.03872, 63 pages.
  • Claude Duhr, "Mathematical aspects of scattering amplitudes". arXiv:1411.7538, 58 pages
  • Tomasz R. Taylor, "A Course in Amplitudes". arXiv:1703.05670, 57 pages

Bootstrap

  • David A. McGady, Laurentiu Rodina, "Higher-spin massless S-matrices in four-dimensions". arXiv:1311.2938, 33 pages.
    • Provides another route to many of the familiar results (like uniqueness of spin-2 field up to some constant factor in the coupling, or absence of interactions for spin j>=3 fields) from relatively straightforward conditions.

Spinor-Helicity Formalism

This is a new-fangled approach which algorithmically computes scattering amplitudes for on-shell processes. As far as I can tell, the computations boil down to recursion relations instead of tricky integrals...which is nice, because computers can do recursion relations way better than they can do integrals. (It is unclear to me whether the formalism extends to off-shell processes, though.)

The standard book on this is Scattering Amplitudes in Gauge Theory and Gravity by Elvang and Huang, though a large portion of it is freely available on arXiv:

  • Clifford Cheung, "TASI Lectures on Scattering Amplitudes". arXiv:1708.03872, 63 pages.
  • Lance J. Dixon, "A brief introduction to modern amplitude methods". arXiv:1310.5353, 48 pages, discusses more topics than just the Spinor-Helicity formalism.
  • Henriette Elvang, Yu-tin Huang, "Scattering Amplitudes". arXiv:1308.1697, 269 pages.
  • Nima Arkani-Hamed, Tzu-Chen Huang, Yu-tin Huang, "Scattering Amplitudes For All Masses and Spins". arXiv:1709.04891, 79 pages.
Raw
reading-list.md

This is just stuff I have yet to classify, but will get around to it...eventually...

Analytic Mechanics

  • Edward Anderson, "Configuration Spaces in Fundamental Physics". arXiv:1503.01507

Ostragradski's Theorem

Pedagogy

  • Serge A. Wagner, "How to introduce physical quantities physically". arXiv:1506.04122

Electromagnetism

  • Roberto De Luca, Marco Di Mauro, Salvatore Esposito, Adele Naddeo, "Feynman's different approach to electrodynamics". arXiv:1902.05799

Quantum Theory

Contextuality

  • Christian de Ronde, "Hilbert Space Quantum Mechanics is Contextual (Reply to R. B. Griffiths)". arXiv:1502.05396

Geometric Quantization

Reviews

  • Mathias Blau, "Symplectic Geometry and Geometric Quantization". eprint [ps.gz]
  • William Gordon Ritter, "Geometric Quantization". arXiv:math-ph/0208008
  • Eugene Lerman "Geometric quantization; a crash course". arXiv:1206.2334

Specialized Topics

  • Jaromir Tosiek, Ruben Cordero, Francisco J. Turrubiates, "An application of the WKB method in deformation quantisation". Eprint arXiv:1502.05497

Molecular Dynamics

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