Books and Papers

John Baez

Here are my books and published papers in chronological order. You can get a lot of these electronically by just clicking on them; whenever possible this will take you to the arXiv. This will also tell you their arXiv number, if that's what you're seeking.


  1. An Introduction to Algebraic and Constructive Quantum Field Theory, with Irving Segal and Zhengfang Zhou, Princeton University Press, 1992. (Out of print. Photocopy available in PDF and DjVu.)

  2. Knots and Quantum Gravity, editor, Oxford University Press, 1994. (Out of print. Text without pictures available in Postscript.)

  3. Gauge Fields, Knots, and Gravity, with Javier Muniain, World Scientific Press, 1994. (The press has released a corrected version, in which known errors in the first version should be fixed.)

  4. Towards Higher Categories, editor, with Peter May, Springer, Berlin, 2009. (Most of the contents of this book are available for free online.)

  5. Infinite-Dimensional Representations of 2-Groups, with Aristide Baratin, Laurent Freidel and Derek Wise, Memoirs of the American Mathematical Society 1032, Providence, Rhode Island, 2012. (Available on the arXiv and from the AMS.)

  6. Quantum Techniques for Stochastic Mechanics, with Jacob Biamonte, World Scientific Press, Singapore, 2018. (Draft available on the arXiv.)


  1. Recursivity in quantum mechanics, Trans. Amer. Math. Soc. 280 (1983), 339-350.

  2. Bell's inequality for C*-algebras, Lett. Math. Phys. 13 (1987), 135-136.

  3. Is life improbable?, Found. Phys. 19 (1989), 91-95.

  4. The global Goursat problem on R × S1, with Zhengfang Zhou, Jour. Funct. Analysis 83 (1989), 364-382.

  5. Scattering and the geometry of the solution manifold of □ f + λ f3 = 0, Jour. Funct. Analysis 83 (1989), 317-332.

  6. Analyticity of scattering for the φ4 theory, with Zhengfang Zhou, Comm. Math. Phys. 124 (1989), 9-21.

  7. Scattering for the Yang-Mills equations, Trans. Amer. Math. Soc. 315 (1989), 823-832.

  8. Wick products of the free Bose field, Jour. Funct. Analysis 86 (1989), 211-225.

  9. Scattering and complete integrability in conformally invariant nonlinear theories, Jour. Math. Phys. 31 (1990), 757-762.

  10. The global Goursat problem and scattering for nonlinear wave equations, with Irving Segal and Zhengfang Zhou, Jour. Funct. Analysis 93 (1990), 239-269.

  11. Conserved quantities for the Yang-Mills equations, Adv. Math. 82 (1990), 126-131.

  12. Scattering and complete integrability in the massive φ4 theory, with Zhengfang Zhou, Jour. Funct. Analysis 94 (1990), 397-414.

  13. Topological lower bound on the energy of a twisted rod, with Rossen Dandoloff, Phys. Lett. A 155 (1991), 145-147.

  14. The vacuum and lightcone quantization of interaction Hamiltonians, Lett. Math. Phys. 21 (1991), 117-121.

  15. Differential calculi on quantum vector spaces with Hecke-type relations, Lett. Math. Phys. 23 (1991), 133-141.

  16. Renormalized oscillator Hamiltonians, with Zhengfang Zhou, Adv. Math. 92 (1992), 106-127.

  17. On quantum fields satisfying a given wave equation, with Zhengfang Zhou, Jour. Funct. Analysis 106 (1992), 439-453.

  18. On the Hopf term in a 2-dimensional sigma model for antiferromagnets, with Alan Bishop and Rossen Dandoloff, Mod. Phys. Lett. B 5 (1991), 2003-2005.

  19. R-commutative geometry and quantization of Poisson algebras, Adv. Math. 95 (1992), 61-91.

  20. Scattering and complete integrability in four dimensions, in Mathematical Aspects of Classical Field Theory, eds. Mark Gotay, Jerrold Marsden and Vincent Moncrief, Contemp. Math. 132, American Mathematical Society, Providence, Rhode Island, 1992, pp. 99-116.

  21. Link invariants of finite type and perturbation theory, Lett. Math. Phys. 26 (1992), 43-51.

  22. Quantum gravity and the algebra of tangles, Classical and Quantum Gravity 10 (1993), 673-694.

  23. An algebraic approach to discrete mechanics, with James Gilliam, Lett. Math. Phys. 31 (1994), 205-212.

  24. Generalized measures in gauge theory, Lett. Math. Phys. 31 (1994), 213-223.

  25. Diffeomorphism-invariant generalized measures on the space of connections modulo gauge transformations, Proceedings of the Conference on Quantum Topology, ed. David N. Yetter, World Scientific Press, Singapore, 1994, pp. 21-43.

  26. Strings, loops, knots and gauge fields, in Knots and Quantum Gravity, ed. J. Baez, Oxford U. Press, Oxford, 1994, pp. 133-168.

  27. Hochschild homology in a braided tensor category, Trans. Amer. Math. Soc. 344 (1994), 885-906.

  28. Strings and two-dimensional QCD for finite N, with Washington Taylor IV, Nucl. Phys. B 426 (1994), 53-70.

  29. Link invariants, holonomy algebras and functional integration, Jour. Funct. Analysis 127 (1995), 108-131.

  30. Topological aspects of spin and statistics of solitons in nonlinear sigma-models, with Michael Ody and William Richter, Jour. Math. Phys. 36 (1995), 108-131.

  31. Higher-dimensional algebra and topological quantum field theory, with James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105.

  32. Quantum gravity hamiltonian for manifolds with boundary, with Javier P. Muniain and Dardo Piriz, Phys. Rev. D 52 (1995), 6840-6845.

  33. Spin network states in gauge theory, Adv. Math. 117 (1996), 253-272.

  34. Spin networks in nonperturbative quantum gravity, in The Interface of Knots and Physics, ed. Louis Kauffman, American Mathematical Society, Providence, Rhode Island, 1996, pp. 167-203.

  35. Four-dimensional BF theory as a topological quantum field theory, Lett. Math. Phys. 38 (1996), 129-143.

  36. Knots and quantum gravity: progress and prospects, in Proceedings of the Seventh Marcel Grossman Meeting on General Relativity, ed. Robert T. Jantzen and G. Mac Keiser, World Scientific Press, 1996, pp. 779-797.

  37. Higher-dimensional algebra I: braided monoidal 2-categories, with Martin Neuchl, Adv. Math. 121 (1996), 196-244.

  38. An introduction to n-categories, in 7th Conference on Category Theory and Computer Science, eds. Eugenio Moggi and Giuseppe Rosolini, Lecture Notes in Computer Science vol. 1290, Springer, Berlin, 1997.

  39. Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189.

  40. Functional integration on the space of connections, with Stephen Sawin, Jour. Funct. Analysis 150 (1997), 1-27.

  41. 2-Tangles, with Laurel Langford, Lett. Math. Phys. 43 (1998), 187-197.

  42. Quantum geometry and black hole entropy, with Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov, Phys. Rev. Lett. 80 (1998), 904-907.

  43. Higher-dimensional algebra III: n-categories and the algebra of opetopes, with James Dolan, Adv. Math. 135 (1998), 145-206.

  44. Spin foam models, Classical and Quantum Gravity 15 (1998), 1827-1858.

  45. Degenerate solutions of general relativity from topological field theory, Comm. Math. Phys. 193 (1998), 219-231.

  46. Diffeomorphism-invariant spin network states, with Stephen Sawin, Jour. Funct. Analysis 158 (1998), 253-266.

  47. Quantization of diffeomorphism-invariant theories with fermions, with Kirill Krasnov, Jour. Math. Phys. 39 (1998), 1251-1271.

  48. Categorification, with James Dolan, in Higher Category Theory, eds. Ezra Getzler and Mikhail Kapranov, Contemp. Math. 230, American Mathematical Society, Providence, Rhode Island, 1998, pp. 1-36.

  49. The quantum tetrahedron in 3 and 4 dimensions, with John Barrett, Adv. Theor. Math. Phys. 3 (1999), 815-850.

  50. An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics, eds. Helmut Gausterer and Harald Grosse, Springer, Berlin, 2000, pp. 25-93.

  51. From finite sets to Feynman diagrams, with James Dolan, in Mathematics Unlimited - 2001 and Beyond, vol. 1, eds. Björn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-50.

  52. Higher-dimensional algebra and Planck-scale physics, in Physics Meets Philosophy at the Planck Length, eds. Craig Callender and Nick Huggett, Cambridge U. Press, Cambridge, 2001, pp. 177-195.

    Also available as a webpage.

  53. Quantum geometry of isolated horizons and black hole entropy, with Abhay Ashtekar and Kirill Krasnov, Adv. Theor. Math. Phys. 4 (2001), 1-94.

  54. Integrability for relativistic spin networks, with John Barrett, Class. Quantum Grav. 18 (2001), 4683–4700.

  55. The octonions, Bull. Amer. Math. Soc. 39 (2002), 145–205. Errata in Bull. Amer. Math. Soc. 42 (2005), 213.

    Also available as a webpage.

  56. Positivity of spin foam amplitudes, with J. Daniel Christensen, Classical and Quantum Gravity 19 (2002), 2291-2306.

  57. Spin foam models of Riemannian quantum gravity, with J. Daniel Christensen, Thomas R. Halford and David C. Tsang, Classical and Quantum Gravity 19 (2002), 4627-4648.

  58. Uncertainty in measurements of distance, with S. Jay Olson, Class. Quantum Grav. 19 (2002), L121-L125.

  59. Asymptotics of 10j symbols, with J. Daniel Christensen and Greg Egan, Classical and Quantum Gravity 19 (2002), 6489-6513.

  60. Spin foam perturbation theory, in Diagrammatic Morphisms and Applications, eds. David Radford, Fernando Souza, and David Yetter, Contemp. Math. 318, American Mathematical Society, Providence, Rhode Island, 2003, pp. 9-21.

  61. Higher-dimensional algebra IV: 2-tangles, with Laurel Langford, Adv. Math. 180 (2003), 705-764.

  62. Higher-dimensional algebra V: 2-groups, with Aaron D. Lauda, Theory and Applications of Categories 12 (2004), 423-491.

  63. Higher-dimensional algebra VI: Lie 2-algebras, with Alissa S. Crans, Theory and Applications of Categories 12 (2004), 492-528.

  64. The meaning of Einstein's equation, with Emory F. Bunn, Amer. Jour. Phys. 73 (2005), 644-652.

    Also available as a webpage.

  65. Quantum quandaries: a category-theoretic perspective, in Structural Foundations of Quantum Gravity, eds. Steven French, Dean Rickles and Juha Saatsi, Oxford U. Press, Oxford, 2006, pp. 240-265.

    Also available as a webpage.

  66. Higher gauge theory, with Urs Schreiber, in Categories in Algebra, Geometry and Mathematical Physics, eds. Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman, Contemp. Math. 431, American Mathematical Society, Providence, Rhode Island, 2007, pp. 7-30.

  67. From loop groups to 2-groups, with Alissa S. Crans, Danny Stevenson and Urs Schreiber, Homotopy, Homology and Applications, 9 (2007), 101-135.

  68. Quantization of strings and branes coupled to BF theory, with Alejandro Perez, Adv. Theor. Math. Phys. 11 (2007), 1-19.

  69. Exotic statistics for strings in 4d BF theory, with Alissa S. Crans and Derek Wise, Adv. Theor. Math. Phys. 11 (2007), 707-749.

  70. Lectures on n-categories and cohomology, with Michael Shulman, in Towards Higher Categories, eds. John Baez and Peter May, Springer, Berlin, 2010, pp. 1-68.

  71. The classifying space of a topological 2-group, with Danny Stevenson, in Algebraic Topology: The Abel Symposium 2007, eds. Nils Baas, Eric Friedlander, Bjørn Jahren and Paul Arne Østvær, Springer, Berlin, 2009.

  72. Categorified symplectic geometry and the classical string, with Alexander E. Hoffnung and Christopher L. Rogers, in Comm. Math. Phys. 293 (2010), 701-715.

  73. Categorified symplectic geometry and the string Lie 2-algebra, with Christopher L. Rogers, in Homotopy, Homology and Applications 12 (2010), 221-236.

  74. The algebra of grand unified theories, with John Huerta, Bull. Amer. Math. Soc. 47 (2010), 483-552.

  75. Division algebras and supersymmetry I, with John Huerta, in Superstrings, Geometry, Topology, and C*-Algebras, eds. Robert Doran, Greg Friedman and Jonathan Rosenberg, Proc. Symp. Pure Math. 81, AMS, Providence, 2010, pp. 65-80.

  76. Higher-dimensional algebra VII: groupoidification, with Alexander E. Hoffnung and Christopher D. Walker, Theory and Applications of Categories 24 (2010), 489-553.

  77. Physics, topology, logic and computation: a Rosetta Stone, with Mike Stay, in New Structures for Physics, ed. Bob Coecke, Lecture Notes in Physics vol. 813, Springer, Berlin, 2011, pp. 95-172.

  78. A prehistory of n-categorical physics, with Aaron D. Lauda, in Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World, ed. Hans Halvorson, Cambridge U. Press, Cambridge, 2011, pp. 13-128.

  79. Convenient categories of smooth spaces, with Alexander E. Hoffnung, Trans. Amer. Math. Soc. 363 (2011), 5789-5825.

  80. An invitation to higher gauge theory, with John Huerta, General Relativity and Gravitation 43 (2011), 2335-2392.

  81. A characterization of entropy in terms of information loss, with Tobias Fritz and Tom Leinster, Entropy 13 (2011), 1945-1957.

  82. Division algebras and supersymmetry II, with John Huerta, Adv. Math. Theor. Phys. 15 (2011), 1373-1410.

  83. Division algebras and quantum theory, Found. Phys. 42 (2012), 819-855.

  84. Algorithmic thermodynamics, with Mike Stay, Math. Struct. Comp. Sci. 22 (2012), 771-787.

  85. A Noether theorem for Markov processes, with Brendan Fong, Jour. Math. Phys. 54 (2013), 013301.

  86. Quantum techniques for studying equilibrium in chemical reaction networks, with Brendan Fong, Journal of Complex Networks 3 (2014), 22-34.

  87. A Bayesian characterization of relative entropy, with Tobias Fritz, Theory and Applications of Categories 29 (2014), 421-456.

  88. G2 and the rolling ball, with John Huerta, Trans. Amer. Math. Soc. 366 (2014), 5257-5293.

  89. Wormholes and entanglement, with Jamie Vicary, Classical and Quantum Gravity 31 (2014), 214007. (11 pages.)

  90. Quantropy, with Blake S. Pollard, Entropy 17 (2015), 772-789.

  91. Teleparallel gravity as a higher gauge theory, with Derek Wise, Comm. Math. Phys. 333 (2015), 153-186.

  92. Categories in control, with Jason Erbele, Theory and Applications of Categories 30 (2015), 836-881.

  93. The Lebesgue universal covering problem, with Karine Bagdasaryan and Philip Gibbs, Journal of Computational Geometry 6 (2015), 288-299.

  94. Relative entropy in biological systems, with Blake S. Pollard, Entropy 18 (2016), 46. (18 pages.)

  95. A compositional framework for Markov processes, with Brendan Fong and Blake S. Pollard, Jour. Math. Phys. 57 (2016), 033301. (30 pages.)

  96. A compositional framework for reaction networks, with Blake S. Pollard, Rev. Math. Phys. 29 (2017), 1750028. (41 pages.)

  97. Operads and phylogenetic trees, with Nina Otter, Theory and Applications of Categories 32 (2017), 1397-1453.

  98. Props in network theory, with Brandon Coya and Franciscus Rebro, Theory and Applications of Categories 33 (2018), 727-783.

  99. Quantum techniques for reaction networks, Adv. Math. Phys. 2018 (2018), 7676309. (9 pages.)

  100. A compositional framework for passive linear networks, with Brendan Fong, Theory and Applications of Categories 33 (2018), 1158-1222.

  101. Coarse-graining open Markov processes, with Kenny Courser, Theory and Applications of Categories 33 (2018), 1223-1268.

  102. Network models from Petri nets with catalysts, with John Foley and Joe Moeller, Compositionality 1, 4 (2019). (15 pages.)

  103. Open Petri nets, with Jade Master, Mathematical Structures in Computer Science 30 (2020), 314-341.

  104. Network models, with John Foley, Blake S. Pollard and Joe Moeller, Theory and Applications of Categories 35 (2020), 700-744.

  105. Enriched Lawvere theories for operational semantics, with Christian Williams, proceedings of Applied Category Theory 2019, Electronic Proceedings of Theoretical Computer Science 323 (2020), 106-135.

  106. Structured cospans, with Kenny Courser, Theory and Applications of Categories 35 (2020), 1771-1822.

  107. Struggles with the continuum, in New Spaces in Physics: Formal and Conceptual Reflections, eds. Mathieu Anel and Gabriel Catren, Cambridge U. Press, Cambridge, 2021, pp. 281-326.

  108. Open systems in classical mechanics, with David Weisbart and Adam M. Yassine, Jour. Math. Phys. 62 (2021), 042902. (24 pages.)

  109. Operads for designing systems of systems, with John Foley, Notices Amer. Math. Soc. 68 (2021), 1005-1007.

  110. Categories of nets, with Fabrizio Genovese, Jade Master and Michael Shulman, in 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), IEEE, Rome, Italy, 2021, pp. 1-13.

  111. The fundamental theorem of natural selection, Entropy, 23 (2021), 1436. (6 pages.)

  112. Structured versus decorated cospans, with Kenny Courser and Christina Vasilakopoulou, Compositionality 4, 3 (2022). (39 pages.)

  113. Rényi entropy and free energy, Entropy 24 (2022), 706. (5 pages.)

  114. Getting to the bottom of Noether's theorem, to appear in the proceedings of Philosophy and Physics of Noether's Theorems: A Centenary Conference on the 1918 Work of Emmy Noether, eds. Bryan W. Roberts and Nicholas Teh.

  115. Compositional thermostatics, with Owen Lynch and Joe Moeller, to appear in Jour. Math. Phys..

  116. Compositional modeling with stock and flow diagrams, with Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Evan Patterson. To appear in Applied Category Theory 2021 as part of Electronic Proceedings of Theoretical Computer Science.

  117. Schur functors and categorified plethysm, with Joe Moeller and Todd Trimble.

  118. A categorical framework for modeling with stock and flow diagrams, with Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Eric Redekopp.

  119. Topological crystals.

  120. Biochemical coupling through emergent conservation laws, with Blake S. Pollard, Jonathan Lorand and Maru Sarazola.


  1. Social structures that enable inventions, in The Greatest Inventions of the Past 2000 Years, ed. John Brockman, Simon and Schuster, 2000, pp. 68-69.
  2. The quantum of area?, Nature 421 (2003), 702-703.
  3. The string-loop war, in What Have You Changed Your Mind About?, ed. John Brockman, Harper, 2009, pp. 156-158.
  4. The Earth — for physicists, PhysicsWorld, August 2009, 22-26.
  5. The strangest numbers in string theory, with John Huerta, Scientific American, May 2011, 60-65. Also in The Best Writing on Mathematics 2012, ed. Mircea Pitici, Princeton U. Press, Princeton, 2012, pp. 50-60.
  6. Monte Carlo methods in climate science, with David Tweed, Math Horizons 21 (2013), 5-8.
  7. From the icosahedron to E8, London Math. Soc. Newsletter 476 (2018), 18-23.
  8. The math that takes Newton into the quantum world, Nautilus, February 28, 2019. Also in The Best Writing on Mathematics 2020, ed. Mircea Pitici, Princeton U. Press, Princeton, 2020.
  9. Qué es la teoría de categorías y cómo se ha convertido en tendencia, El PaĆ­s, November 8, 2019. (English version: Why is category theory a trending topic?)
  10. Is net zero emissions an impossible goal?, Nautilus, November 28, 2019.
  11. The tenfold way, Notices Amer. Math. Soc. 67 (2020), 1599-1601.

  12. This Week's Finds in Mathematical Physics (1–50), 242 pages, 2021.
  13. The joy of condensed matter physics, Nautilus, February 25, 2021.
  14. The Brownian map, Notices Amer. Math. Soc. 68 (2021), 801-803.

  15. The Gauss–Lucas theorem, Notices Amer. Math. Soc. 68 (2021), 1988-1989.

  16. Applied category theory in chemistry, computing and social networks, with Simon Cho, Daniel Cicala, Nina Otter and Valeria de Paiva, Notices Amer. Math. Soc. 69 (2022), 292-296.
  17. The Kuramoto–Sivashinsky equation, with Steve Huntsman and Cheyne Weis, Notices Amer. Math. Soc. 69 (2022), 1581-1583.
  18. Isbell duality, Notices Amer. Math. Soc. 70 (2022), 140-141.
  19. The icosidodecahedron, to appear in Notices Amer. Math. Soc..

Book Reviews

  1. The Physical Basis of the Direction of Time, by H. D. Zeh, review in Math. Intelligencer 16 (1994), 72-75.

  2. On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, by John H. Conway and Derek A. Smith, review in Bull. Amer. Math. Soc. 42 (2005), 229-243.

  3. Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths, by Eugenia Cheng, review in London Math. Soc. Newsletter 451 (2015), 34.

  4. Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, edited by Joseph Kouneiher, review in Notices Amer. Math. Soc. 66 (November 2019), 1690-1692.


Of making books there is no end, and much study is a weariness of the flesh... - Ecclesiastes 12:12

© 2021 John Baez