Skip to content

Bibliography

Jump to bottom Edit New page
Alex edited this page Jan 23, 2015 · 30 revisions

Contents

  1. Classical & Analytical Mechanics
  2. Gauge Systems
  3. Reduced Phase Space
  4. Yang-Mills
  5. Chern-Simons
  6. General Relativity
  7. Spin-2 Formalism
  8. Newton-Cartan Formalism
  9. Canonical Formalism
  10. Mathematical Relativity 1. Positive Mass Theorem 2. Positive Energy Theorem 3. Energy Conditions
  11. Numerical Relativity
  12. Empirical Analysis
  13. Alternatives
  14. Quantum Mechanics
  15. S-Matrix Stuff
  16. Quantum Field Theory
  17. Schrodinger Picture
  18. Quantum Fields in Curved Spacetime
  19. Renormalization 1. Renormalization Group 2. Asymptotic Safety
  20. Quantization of Gauge Systems
  21. Mathematics
  22. Collections of Lectures
# Classical & Analytical Mechanics 1. Simon J.A. Malham, "An introduction to Lagrangian and Hamiltonian mechanics". [Eprint](http://www.macs.hw.ac.uk/~simonm/mechanics.pdf), 56 pages. 2. Daniel Arovas, "Lecture Notes on Classical Mechanics". [Eprint](http://www-physics.ucsd.edu/students/courses/fall2010/physics200a/LECTURES/200_COURSE.pdf), 453 pages. 3. JE Marsden, "Generalized Hamiltonian Mechanics". *Archive for Rational Mechanics and Analysis* **28** no. 5 (1968) 323-361, [eprint](http://authors.library.caltech.edu/19627/1/Ma1968%284%29.pdf). 4. Gerald Jay Sussman and Jack Wisdom *Structure and Interpretation of Classical Mechanics*. [Eprint](http://mitpress.mit.edu/sites/default/files/titles/content/sicm/book.html)

Newtonian Mechanics

  1. David Morin's book, I highly don't recommend it --- but I was forced to obtain a copy for a course.
  2. Peter Lynch, "The Not-so-simple Pendulum: Balancing a Pencil on its Point". Eprint arXiv:1406.1125 discusses how badly Morin botched his explanations of classical behaviour, demonstrating further Morin doesn't understand the classical limit of quantum systems. (C.f., Morin's exercise 3.13, he remarks "This smallness of this answer is quite amazing. It is remarkable that a quantum effect on a macroscopic object can produce an everyday value for a time scale.")
# Gauge Systems 1. Henneaux and Teitelboim's *Quantization of Gauge Systems* 2. Sergei V. Shabanov, "Geometry of the physical phase space in quantum gauge models". Eprint [arXiv:hep-th/0002043](http://arxiv.org/abs/hep-th/0002043) 3. Ingemar Bengtsson, "Constrained Hamiltonian Systems". [Lecture Notes](http://www.fysik.su.se/~ingemar/Nr13.pdf) 4. PAM Dirac, "Generalized Hamiltonian dynamics". *Canadian Journal of Mathematics* **2** (1950) 129-148; [Eprint](http://cms.math.ca/cjm/v2/cjm1950v02.0129-0148.pdf) 5. PAM Dirac, "The Hamiltonian form of field dynamics". *Canadian Journal of Mathematics* **3** (1951) 1-23; [Eprint](http://cms.math.ca/cjm/v3/cjm1951v03.0001-0023.pdf) 6. R. Jackiw, "Non-Yang--Mills Gauge Theories". Eprint [arXiv:hep-th/9705028](http://arxiv.org/abs/hep-th/9705028). ## Reduced Phase Space 1. J M Pons, D C Salisbury, L C Shepley, "Reduced phase space: quotienting procedure for gauge theories". *J.Phys.A* **32** (1999) 419--430, [arXiv:math-ph/9811029](http://arxiv.org/abs/math-ph/9811029) ## Yang-Mills 1. M. Laufer, P. Orland "The Metric of Yang-Mills Orbit Space on the Lattice". *Phys. Rev. D* **88** (2013) 065018, [arXiv:1203.5134](http://arxiv.org/abs/1203.5134) 2. Andrew Strominger, "Asymptotic Symmetries of Yang-Mills Theory". Eprint [arXiv:1308.0589](http://arxiv.org/abs/1308.0589) ## Chern-Simons 1. Térence Delsate, David Hilditch, Helvi Witek, "The Initial Value Formulation of Dynamical Chern-Simons Gravity". *Phys. Rev. D* **91** (2015) 024027. Eprint [arXiv:1407.6727](http://arxiv.org/abs/1407.6727) DOI:[10.1103/PhysRevD.91.024027](http://dx.doi.org/10.1103/PhysRevD.91.024027) 2. R. Jackiw, S.-Y. Pi, "Chern-Simons Modification of General Relativity". *Phys.Rev. D* **68** (2003) 104012. Eprint [arXiv:gr-qc/0308071](http://arxiv.org/abs/gr-qc/0308071) DOI:[10.1103/PhysRevD.68.104012](http://dx.doi.org/10.1103/PhysRevD.68.104012) 3. Gerald V. Dunne, "Self-Dual Chern-Simons Theories". Eprint [arXiv:hep-th/9410065](http://arxiv.org/abs/hep-th/9410065) 4. Gerald V. Dunne, "Aspects of Chern-Simons Theory". Les Houches Lectures 1998, eprint [arXiv:hep-th/9902115](http://arxiv.org/abs/hep-th/9902115). 5. Jorge Zanelli, "Chern-Simons Forms in Gravitation Theories". *Class. & Quantum Grav.* **29** (2012) 133001. Eprint [arXiv:1208.3353](http://arxiv.org/abs/1208.3353). 6. J. M. F. Labastida, "Chern-Simons Gauge Theory: Ten Years After". *AIP Conf. Proc.* **484**, 1 (1999). Eprint [arXiv:hep-th/9905057](http://arxiv.org/abs/hep-th/9905057), DOI:[10.1063/1.59663](http://dx.doi.org/10.1063/1.59663) # General Relativity

There is a lot of references I could put down, so instead I'll just mark up my "to read" list.

## Spin-2 Formalism 1. Jessica Frank, Michael Rauch, Dieter Zeppenfeld, "Spin-2 Resonances in Vector-Boson-Fusion Processes at NLO QCD". *Phys. Rev. D* **87** (2013) 055020 (2013). Eprint [arXiv:1211.3658](http://arxiv.org/abs/1211.3658) DOI:[10.1103/PhysRevD.87.055020](http://dx.doi.org/10.1103/PhysRevD.87.055020) 2. Yurij V. Baryshev, "Field Theory of Gravitation: Desire and Reality". *Gravitation* **2** (1996) 69-81. Eprint [arXiv:gr-qc/9912003](http://arxiv.org/abs/gr-qc/9912003), 17 pages 3. T. Padmanabhan, "From Gravitons to Gravity: Myths and Reality". *Int.J.Mod.Phys.D* **17** (2008) 367-398. Eprint [arXiv:gr-qc/0409089](http://arxiv.org/abs/gr-qc/0409089). DOI:[10.1142/S0218271808012085](http://dx.doi.org/10.1142/S0218271808012085). ## Spinors in GR 1. Jorge G. Cardoso, "The Classical World and Spinor Formalisms of General Relativity". Eprint [arXiv:1004.5150](http://arxiv.org/abs/1004.5150), 77pp. ## Newton-Cartan Formalism
  1. Roel Andringa, Eric Bergshoeff, Sudhakar Panda, M. de Roo, "Newtonian Gravity and the Bargmann Algebra". Class.Quant.Grav. 28 (2011) 105011, arXiv:1011.1145
  2. Joy Christian, "Exactly Soluble Sector of Quantum Gravity". Phys.Rev.D 56 (1997) 4844-4877, arXiv:gr-qc/9701013
## Canonical Formalism 1. R. Arnowitt, S. Deser, CW Misner, "The Dynamics of General Relativity". Eprint [arXiv:gr-qc/0405109](http://arxiv.org/abs/gr-qc/0405109) 2. Stephen C. Anco, Roh S. Tung "Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions". *J.Math.Phys.* **43** (2002) 3984--4019, [arXiv:gr-qc/0109014](http://arxiv.org/abs/gr-qc/0109014). 3. A.M. Frolov, N. Kiriushcheva, S.V. Kuzmin, "On canonical transformations between equivalent Hamiltonian formulations of General Relativity". *Gravitation and Cosmology* **17** no.4 (2011) 314--323, doi:[10.1134/S0202289311040049](http://dx.doi.org/10.1134/S0202289311040049), [arXiv:0809.1198](http://arxiv.org/abs/0809.1198) 4. Qing Han, Marcus Khuri "The Conformal Flow of Metrics and the General Penrose Inequality". Eprint [arXiv:1409.0067](http://arxiv.org/abs/1409.0067), 13 pp.

"Util Papers"

Just as lisp has "util functions", helper functions that enable one to write programs, I'll collate some "helper papers".

  1. Francesco Bonsante, Andrea Seppi, "On Codazzi tensors on a hyperbolic surface and flat Lorentzian geometry". Eprint arXiv:1501.04922, 49 pages.

Mass and Angular Momentum

  1. Leo Brewin, "A simple expression for the ADM mass". Gen.Rel.Grav. 39 (2007) 521-528, arXiv:gr-qc/0609079
  2. Christopher Nerz, "Time evolution of ADM and CMC center of mass in general relativity". Eprint arXiv:1312.6274
  3. Levi Lopes de Lima, Frederico Girão, "The ADM mass of asymptotically flat hypersurfaces". Eprint arXiv:1108.5474, 20 pages.
  4. J.L. Jaramillo, E. Gourgoulhon, "Mass and Angular Momentum in General Relativity". Eprint arXiv:1001.5429, 41 pages.
## Mathematical Relativity 1. Robert Bartnik, "Phase Space for the Einstein Equations". *Communications in Analysis and Geometry* **13** no.5 (2005) 845--885, [arXiv:gr-qc/0402070](http://arxiv.org/abs/gr-qc/0402070) 2. Stephen McCormick, "The Phase Space for the Einstein-Yang-Mills Equations and the First Law of Black Hole Thermodynamics". [arXiv:1302.1237](http://arxiv.org/abs/1302.1237) NB: generalizes Bartnik's technique (previous entry) to the Einstein-Yang-Mills system. ### Positive Mass Theorem 1. Piotr T. Chruściel, Tim-Torben Paetz, "The mass of light-cones". *Classical and Quantum Gravity* **31** no.10 (2014) 102001, [arXiv:1401.3789](http://arxiv.org/abs/1401.3789) ### Positive Energy Theorem 1. Piotr T. Chrusciel, Gregory J. Galloway, "A Poor Man's Positive Energy Theorem". *Class.Quant.Grav.* **21** (2004) L59-L63, [arXiv:gr-qc/0402106](http://arxiv.org/abs/gr-qc/0402106) 2. Sergio Dain, "Positive energy theorems in General Relativity". A chapter in *The Springer Handbook of Spacetime* (eds. A Ashtekar and V Petkov), [arXiv:1302.3405](http://arxiv.org/abs/1302.3405) 3. James M. Nester, Roh-Suan Tung, Yuan Zhong Zhang "Ashtekar's New Variables and Positive Energy". *Class.Quant.Grav.* **11** (1994) 757--766, doi:[10.1088/0264-9381/11/3/024](http://dx.doi.org/10.1088/0264-9381/11/3/024), [arXiv:gr-qc/9401004](http://arxiv.org/abs/gr-qc/9401004) ### Energy Conditions 1. Erik Curiel, "A Primer on Energy Conditions". Eprint [arXiv:1405.0403](http://arxiv.org/abs/1405.0403) 2. T. Roman, "Quantum stress-energy tensors and the weak energy condition". *Phys.Rev. D* **33** (1986) 3526 DOI:[10.1103/PhysRevD.33.3526](http://journals.aps.org/prd/abstract/10.1103/PhysRevD.33.3526) 3. C.J. Fewster, T.A. Roman, "Null energy conditions in quantum field theory". *Phys.Rev. D* **67* (2003) 044003. Eprint [arXiv:gr-qc/0209036](http://arxiv.org/abs/gr-qc/0209036). DOI:[10.1103/PhysRevD.67.044003](http://dx.doi.org/10.1103/PhysRevD.67.044003) 4. Christopher J Fewster, "Energy Inequalities in Quantum Field Theory". Eprint [arXiv:math-ph/0501073](http://arxiv.org/abs/math-ph/0501073) ## Numerical Relativity 1. Luis Lehner, "Numerical Relativity: A review". *Class.Quant.Grav.* **18** (2001) R25-R86, [arXiv:gr-qc/0106072](http://arxiv.org/abs/gr-qc/0106072) 2. Eric Gourgoulhon, "3+1 Formalism and Bases of Numerical Relativity". [arXiv:gr-qc/0703035](http://arxiv.org/abs/gr-qc/0703035), 220 pages and 25 figures 3. Hirotada Okawa, "Initial Conditions for Numerical Relativity -- Introduction to numerical methods for solving elliptic PDEs". Eprint [arXiv:1308.3502](http://arxiv.org/abs/1308.3502), 40 pages. 4. Vitor Cardoso, Leonardo Gualtieri, Carlos Herdeiro, Ulrich Sperhake, "Exploring New Physics Frontiers Through Numerical Relativity". *Living Reviews in Relativity*. Eprint [arXiv:1409.0014](http://arxiv.org/abs/1409.0014), 154 pages. ## Empirical Analysis 1. Piotr Jaranowski and Andrzej Królak, "Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case". *Living Rev. Relativity* **15** (2012), 4 [eprint](http://relativity.livingreviews.org/Articles/lrr-2012-4/) 2. Curt Cutler and Kip S. Thorne, "An Overview of Gravitational-Wave Sources". Eprint [arXiv:gr-qc/0204090](http://arxiv.org/abs/gr-qc/0204090) ## Alternatives 1. Flavio Mercat, "A Shape Dynamics Tutorial". Eprint [arXiv:1409.0105](http://arxiv.org/abs/1409.0105), 71pp. 2. Vladimir Dzhunushaliev, Vladimir Folomeev, Burkhard Kleihaus, Jutta Kunz, "Modified gravity from the nonperturbative quantization of a metric". Eprint [arXiv:1501.00886](http://arxiv.org/abs/1501.00886), 7pp. # Quantum Mechanics ## S-Matrix Stuff 1. Yogesh Dandekar, Mangesh Mandlik, Shiraz Minwalla, "Poles in the S-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics". Eprint [arXiv:1407.1322](http://arxiv.org/abs/1407.1322) [hep-th] 2. Alan R. White, "The Past and Future of S-Matrix Theory". Eprint [arXiv:hep-ph/0002303](http://arxiv.org/abs/hep-ph/0002303), 43 pages # Quantum Field Theory
  1. Peter Arnold, Paul Romatschke, Wilke van der Schee, "Absence of a local rest frame in far from equilibrium quantum matter". Eprint arXiv:1408.2518, 5 pages.
  2. Qingchun Ji, Ke Zhu, "Solvability of the Dirac equation". Eprint arXiv:1407.6936
  3. D.S. Kaparulin, S.L. Lyakhovich, A.A. Sharapov, "Classical and quantum stability of higher-derivative dynamics". Eprint arXiv:1407.8481, 39 pages.
## Schrodinger Picture 1. Sebastian Krug, "The Yang-Mills Vacuum Wave Functional in 2+1 Dimensions". Eprint [arXiv:1404.7005](http://arxiv.org/abs/1404.7005), PhD thesis, 229 pages. 2. I.V. Kanatchikov, "Precanonical Quantization and the Schroedinger Wave Functional." *Phys.Lett. A* **283** (2001) 25--36, [arXiv:hep-th/0012084](http://arxiv.org/abs/hep-th/0012084) 3. D.V. Long, G.M. Shore, "The Schrodinger Wave Functional and Vacuum States in Curved Spacetime." *Nucl.Phys. B* **530** (1998) 247--278, [arXiv:hep-th/9605004](http://arxiv.org/abs/hep-th/9605004) 4. H. Reinhardt, C. Feuchter, "On the Yang-Mills wave functional in Coulomb gauge." *Phys.Rev. D* **71** (2005) 105002, [arXiv:hep-th/0408237](http://arxiv.org/abs/hep-th/0408237) 5. Brian Hatfield, *Quantum Field Theory of Point Particles and Strings*. Addison Wesley Longman, 1992. See Chapter 10 "Free Fields in the Schrodinger Representation". 6. D.V.Long, G.M.Shore, "The Schrodinger Wave Functional and Vacuum States in Curved Spacetime". *Nucl.Phys. B* **530** (1998) 247--278, [arXiv:hep-th/9605004](arxiv.org/abs/hep-th/9605004) 7. George Tiktopoulos, "Variational Wave Functionals in Quantum Field Theory". *Phys.Rev. D* **57** (1998) 6429-6440. Eprint [arXiv:hep-th/9705230](http://arxiv.org/abs/hep-th/9705230). Discusses the Rayleigh-Schrodinger approximation. 8. Alejandro Corichi, Jeronimo Cortez, Hernando Quevedo "On the Relation Between Fock and Schroedinger Representations for a Scalar Field". Eprint [arXiv:hep-th/0202070](http://arxiv.org/abs/hep-th/0202070). Corichi appears to have done quite a bit of work related to the functional Schrodinger picture in QFT. ## Quantum Fields in Curved Spacetime 1. Christopher J. Fewster, "Lectures on quantum field theory in curved spacetime". Lecture note no. 30 (2008) 62 pages, [eprint](http://www.science.unitn.it/~moretti/Fewsternotes.pdf) 2. Thomas-Paul Hack, "On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications". PhD Thesis, 262 pages, [arXiv:1008.1776](http://arxiv.org/abs/arXiv:1008.1776). 3. RM Wald, *Quantum field theory in curved spacetime and black hole thermodynamics* 4. Marcos Brum, "Explicit construction of Hadamard states for Quantum Field Theory in curved spacetimes". PhD thesis, 129+xvi pages, Eprint [arXiv:1407.3612](http://arxiv.org/abs/1407.3612) [gr-qc] ## Renormalization ### Renormalization Group 1. Janos Polonyi, "Lectures on the functional renormalization group method". *Central Eur.J.Phys.* **1** (2003) 1-71. Eprint [arXiv:hep-th/0110026](http://arxiv.org/abs/hep-th/0110026), 47 pages. 2. Holger Gies, "Introduction to the functional RG and applications to gauge theories". Eprint [arXiv:hep-ph/0611146](http://arxiv.org/abs/hep-ph/0611146), 60 pages. 3. Bertrand Delamotte, "An Introduction to the Nonperturbative Renormalization Group". Eprint [arXiv:cond-mat/0702365](http://arxiv.org/abs/cond-mat/0702365), 56 pages ### Asymptotic Safety 1. R. Percacci, "Asymptotic Safety". In *Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter*, ed. D. Oriti, Cambridge University Press. Eprint [arXiv:0709.3851](http://arxiv.org/abs/0709.3851) 2. R. Percacci, "A short introduction to asymptotic safety". Eprint [arXiv:1110.6389](http://arxiv.org/abs/1110.6389), 18 pages. 3. Sandor Nagy, "Lectures on renormalization and asymptotic safety". *Annals of Physics* **350** (2014), pp. 310-346. Eprint [arXiv:1211.4151](http://arxiv.org/abs/1211.4151) DOI:[10.1016/j.aop.2014.07.027](http://dx.doi.org/10.1016/j.aop.2014.07.027) 4. Kevin Falls, Daniel F. Litim, Konstantinos Nikolakopoulos, Christoph Rahmede "Further evidence for asymptotic safety of quantum gravity". Eprint [arXiv:1410.4815](http://arxiv.org/abs/1410.4815) 5. Kevin Falls, "On the renormalisation of Newton's constant". [arXiv:1501.05331](http://arxiv.org/abs/1501.05331), 20 pages.

Toy Models

  1. Jens Braun, Holger Gies, Daniel D. Scherer, "Asymptotic safety: a simple example". Phys.Rev.D 83 (2011) 085012. Eprint arXiv:1011.1456 DOI:10.1103/PhysRevD.83.085012
  2. J. Kovacs, S. Nagy, K. Sailer, "Asymptotic safety in the sine-Gordon model". Eprint arXiv:1408.2680, 8 pages.
  3. Björn H. Wellegehausen, Daniel Körner, Andreas Wipf, "Asymptotic safety on the lattice: The Nonlinear O(N) Sigma Model". Eprint arXiv:1402.1851, 16 pages.
  4. Daniel F. Litim, Francesco Sannino, "Asymptotic safety guaranteed". Eprint arXiv:1406.2337, 31 pages.
  5. Alessandro Codello, YouTube lecture "Introduction to asymptotic safety", 1hr14min. Given at CP3 at the University of Southern Denmark, 28 August 2014.
  6. P. Donà, Astrid Eichhorn, Roberto Percacci, "Consistency of matter models with asymptotically safe quantum gravity". Will be in the Proceedings of Theory Canada 9, eprint arXiv:1410.4411. Constrains the possible choices of matter (esp. spin-3/2 particles) assuming gravity is asymptotically safe.
  7. Pietro Donà, Astrid Eichhorn, Roberto Percacci "Matter matters in asymptotically safe quantum gravity". Eprint arXiv:1311.2898 [hep-th]
# Quantization of Gauge Systems Usually the canonical quantization scheme is avoided, because...well, it's a nightmare on a good day. The path integral scheme usually takes the BRST approach.
  1. Henneaux and Teitelboim's Quantization of Gauge Systems

Constraint Algebra

  1. Waldemar Schulgin, Jan Troost, "The Algebra of Diffeomorphisms from the World Sheet". Eprint arXiv:1407.1385 [hep-th]

Geometric Schemes

Remember geometric quantization weakens the condition that Poisson brackets are "quantized" into commutators.

  1. M.Nakamura, "Star-product Quantization in Second-class Constraint Systems". Eprint arXiv:1108.4108
# Mathematics 1. Duokui Yan, Rongchang Liu, Geng-zhe Chang, "A type of multiple integral with loggamma function". Eprint [arXiv:1404.5143](http://arxiv.org/abs/1404.5143) 2. Tanya Khovanova, "Clifford Algebras and Graphs". Eprint [arXiv:0810.3322](http://arxiv.org/abs/0810.3322) 3. Uwe Bäsel, "A remark concerning sinc integrals". Eprint [arXiv:1404.5413](http://arxiv.org/abs/1404.5413)

Classical Analysis

  1. Alexander Plakhov, "Newton's problem of minimal resistance under the single-impact assumption". Eprint arXiv:1405.0122

Differential Geometry

  1. Andreas Kriegl, Peter W. Michor, Armin Rainer, "An exotic zoo of diffeomorphism groups on Rn". Eprint arXiv:1404.7033
  2. Arthur Besse, Einstein Manifolds. Springer-Verlag, 1987.
  3. Fernando Galaz-Garcia, Luis Guijarro, "Every point in a Riemmanian manifold is critical". Eprint arXiv:1408.4777, 7 pages.

Lie Groups

  1. Jan Milan Eyni, "The Frobenius theorem for Banach distributions on infinite-dimensional manifolds and applications in infinite-dimensional Lie theory". Eprint arXiv:1407.3166 [math.GR]
  2. Karl-Hermann Neeb, "Semibounded representations and invariant cones in infinite dimensional Lie algebras". Eprint arXiv:0911.4412
  3. Yuri Neretin, "Structures of boson and fermion Fock spaces in the space of symmetric functions". Acta Applicandae Mathematica 81 no.1 (2004) e233-268, Eprint arXiv:math-ph/0306077
  4. Yuri Neretin, "A remark on representations of infinite symmetric groups". J. Math. Sci. 190 (2013) 464--467, Eprint arXiv:1204.4198

Infinite-Dimensional Integrals

  1. Iztok Banic, "Integrations on rings". Eprint arXiv:1406.3061, 15 pages.
  2. Irving Segal, "Algebraic integration theory". Bull. Amer. Math. Soc. 71 No. 3 (1965), 419-489. Eprint
# Collections of Lectures 1. Richard Fitzpatrick has many lecture notes assembled on his [page](http://farside.ph.utexas.edu/teaching.html) 2. Roger D. Blandford and Kip Thorne's "Applications of Classical Physics" [CalTech Phy136](http://www.pma.caltech.edu/Courses/ph136/yr2012/)
Add a custom footer
Add a custom sidebar

Clone this wiki locally