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.
Books

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.)

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

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.)

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

InfiniteDimensional
Representations of 2Groups, 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.)

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

What is Entropy?, 2024.
Papers

Recursivity in quantum
mechanics, Trans. Amer. Math. Soc. 280 (1983),
339350.

Bell's inequality for C*algebras,
Lett. Math. Phys. 13 (1987), 135136.

Is life improbable?, Found. Phys.
19 (1989), 9195.

The global Goursat problem on
R × S^{1}, with Zhengfang Zhou, Jour.
Funct. Analysis 83 (1989), 364382.

Scattering and the geometry of the
solution manifold of □ f + λ f^{3} = 0,
Jour. Funct. Analysis 83 (1989), 317332.

Analyticity of scattering for the φ^{4} theory,
with Zhengfang Zhou, Comm. Math. Phys. 124 (1989), 921.

Scattering for the YangMills equations,
Trans. Amer. Math. Soc. 315 (1989), 823832.

Wick products of the free Bose field,
Jour. Funct. Analysis 86 (1989), 211225.

Scattering and complete integrability in conformally invariant nonlinear
theories, Jour. Math. Phys. 31 (1990), 757762.

The global Goursat problem and scattering for nonlinear wave
equations, with Irving Segal and Zhengfang Zhou,
Jour. Funct. Analysis 93 (1990), 239269.

Conserved quantities for the YangMills equations, Adv. Math.
82 (1990), 126131.

Scattering and complete integrability in the massive φ^{4}
theory, with Zhengfang Zhou, Jour. Funct. Analysis 94
(1990), 397414.

Topological lower bound on the energy of a twisted rod,
with Rossen Dandoloff, Phys. Lett. A 155 (1991), 145147.

The vacuum and lightcone quantization of interaction Hamiltonians,
Lett. Math. Phys. 21 (1991), 117121.

Differential calculi on quantum vector spaces with Hecketype
relations, Lett. Math. Phys. 23 (1991), 133141.

Renormalized oscillator Hamiltonians,
with Zhengfang Zhou, Adv. Math. 92 (1992), 106127.

On quantum fields satisfying a given wave equation, with Zhengfang
Zhou, Jour. Funct. Analysis 106 (1992), 439453.

On the Hopf term in a 2dimensional sigma model
for antiferromagnets, with Alan Bishop and Rossen Dandoloff,
Mod. Phys. Lett. B 5 (1991), 20032005.

Rcommutative geometry and quantization of Poisson algebras,
Adv. Math. 95 (1992), 6191.

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. 99116.

Link invariants of finite type and perturbation theory,
Lett. Math. Phys. 26 (1992), 4351.

Quantum gravity and the algebra of tangles,
Classical and Quantum Gravity 10 (1993), 673694.

An algebraic approach to discrete mechanics, with James Gilliam,
Lett. Math. Phys. 31 (1994), 205212.

Generalized measures in gauge theory, Lett. Math. Phys. 31
(1994), 213223.

Diffeomorphisminvariant 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. 2143.

Strings, loops, knots and gauge fields, in Knots and Quantum
Gravity, ed. J. Baez, Oxford U. Press, Oxford, 1994, pp. 133168.

Hochschild homology in a braided tensor category,
Trans. Amer. Math. Soc. 344 (1994), 885906.

Strings and twodimensional QCD for finite N, with Washington Taylor
IV, Nucl. Phys. B 426 (1994), 5370.

Link invariants, holonomy algebras and functional integration,
Jour. Funct. Analysis 127 (1995), 108131.

Topological aspects of spin and statistics of solitons in nonlinear
sigmamodels, with Michael Ody and William Richter, Jour.
Math. Phys. 36 (1995), 108131.

Higherdimensional algebra and topological quantum field theory, with
James Dolan, Jour. Math. Phys. 36 (1995), 60736105.

Quantum gravity hamiltonian for manifolds with boundary, with
Javier P. Muniain and Dardo Piriz, Phys. Rev. D 52 (1995),
68406845.

Spin network states in gauge theory, Adv. Math. 117
(1996), 253272.

Spin networks in nonperturbative quantum gravity, in
The Interface of Knots and Physics, ed. Louis Kauffman, American
Mathematical Society, Providence, Rhode Island, 1996,
pp. 167203.

Fourdimensional BF theory as a topological quantum field theory,
Lett. Math. Phys. 38 (1996), 129143.

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. 779797.

Higherdimensional algebra I: braided monoidal 2categories, with Martin
Neuchl, Adv. Math. 121 (1996), 196244.

An introduction to ncategories, 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.

Higherdimensional algebra II: 2Hilbert spaces,
Adv. Math. 127 (1997), 125189.

Functional integration on the space of connections, with
Stephen Sawin, Jour. Funct. Analysis 150 (1997), 127.

2Tangles, with Laurel Langford, Lett. Math. Phys.
43 (1998), 187197.

Quantum geometry and black hole entropy,
with Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov,
Phys. Rev. Lett. 80 (1998), 904907.

Higherdimensional algebra III: ncategories
and the algebra of opetopes,
with James Dolan, Adv. Math. 135 (1998), 145206.

Spin foam models, Classical and Quantum Gravity 15 (1998),
18271858.

Degenerate solutions of general relativity from topological
field theory, Comm. Math. Phys. 193 (1998), 219231.

Diffeomorphisminvariant spin network states, with Stephen
Sawin, Jour. Funct. Analysis 158 (1998), 253266.

Quantization of diffeomorphisminvariant theories with fermions,
with Kirill Krasnov, Jour. Math. Phys. 39 (1998), 12511271.

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. 136.

The quantum tetrahedron
in 3 and 4 dimensions, with John Barrett,
Adv. Theor. Math. Phys. 3 (1999), 815850.

An introduction to spin
foam models of BF theory and quantum gravity, in
Geometry and Quantum Physics, eds. Helmut Gausterer and Harald
Grosse, Springer Lecture Notes in Physics 543,
Springer, Berlin, 2000, pp. 2593.

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. 2950.

Higherdimensional algebra and Planckscale physics, in Physics
Meets Philosophy at the Planck Length, eds. Craig Callender and
Nick Huggett, Cambridge U. Press, Cambridge, 2001, pp. 177195.
Also available as a webpage.

Quantum geometry of
isolated horizons and black hole entropy, with Abhay Ashtekar and
Kirill Krasnov, Adv. Theor. Math. Phys. 4 (2001), 194.

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

The octonions,
Bull. Amer. Math. Soc. 39 (2002), 145–205.
Errata in Bull. Amer. Math. Soc. 42 (2005), 213.
Also available as a webpage.

Positivity of spin foam
amplitudes, with J. Daniel Christensen, Classical and Quantum
Gravity 19 (2002), 22912306.

Spin
foam models of Riemannian quantum gravity,
with J. Daniel Christensen, Thomas R. Halford and David C. Tsang,
Classical and Quantum Gravity 19 (2002), 46274648.

Uncertainty in
measurements of distance, with S. Jay Olson, Class. Quantum
Grav. 19 (2002), L121L125.

Asymptotics
of 10j symbols, with J. Daniel Christensen and Greg Egan,
Classical and Quantum Gravity 19 (2002), 64896513.

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. 921.

Higherdimensional algebra IV: 2tangles, with Laurel Langford,
Adv. Math. 180 (2003), 705764.

Higherdimensional
algebra V: 2groups, with Aaron D. Lauda,
Theory
and Applications of Categories 12 (2004), 423491.

Higherdimensional
algebra VI: Lie 2algebras, with Alissa S. Crans,
Theory
and Applications of Categories 12 (2004), 492528.

The meaning of
Einstein's equation, with Emory F. Bunn, Amer. Jour. Phys.
73 (2005), 644652.
Also available as a webpage.

Quantum quandaries:
a categorytheoretic perspective, in
Structural Foundations of Quantum Gravity,
eds. Steven French, Dean Rickles and Juha Saatsi, Oxford U. Press,
Oxford, 2006, pp. 240265.
Also available as a webpage.

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. 730.

From loop groups
to 2groups, with Alissa S. Crans, Danny Stevenson and Urs Schreiber,
Homotopy,
Homology and Applications, 9 (2007), 101135.
Erratum to "From loop groups to 2groups", Homotopy, Homology and Applications, 25 (2023), 403405.

Quantization
of strings and branes coupled to BF theory, with Alejandro Perez,
Adv. Theor.
Math. Phys. 11 (2007), 119.

Exotic statistics for
strings in 4d BF theory, with Alissa S. Crans and Derek
Wise, Adv.
Theor. Math. Phys. 11 (2007), 707749.

Lectures on
ncategories and cohomology, with Michael Shulman,
in Towards Higher Categories, eds.
John Baez and Peter May, Springer, Berlin, 2010, pp. 168.

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

Categorified symplectic
geometry and the classical string, with Alexander E. Hoffnung and
Christopher L. Rogers, in Comm. Math. Phys. 293 (2010), 701715.

Categorified symplectic
geometry and the string Lie 2algebra, with Christopher L. Rogers,
in Homotopy,
Homology and Applications 12 (2010), 221236.

The algebra of grand unified
theories, with John Huerta,
Bull. Amer. Math. Soc. 47 (2010), 483552.

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. 6580.

Higherdimensional algebra
VII: groupoidification, with Alexander E. Hoffnung and Christopher
D. Walker, Theory and
Applications of Categories 24 (2010), 489553.

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. 95172.

A prehistory of ncategorical
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. 13128.

Convenient categories
of smooth spaces, with Alexander E. Hoffnung, Trans. Amer.
Math. Soc. 363 (2011), 57895825.

An
invitation to higher gauge theory, with John Huerta, General
Relativity and Gravitation 43 (2011), 23352392.

A characterization of
entropy in terms of information loss, with Tobias Fritz and Tom
Leinster, Entropy
13 (2011), 19451957.

Division algebras and
supersymmetry II, with John Huerta, Adv. Math. Theor.
Phys. 15 (2011), 13731410.

Division algebras and
quantum theory, Found. Phys. 42 (2012), 819855.

Algorithmic thermodynamics,
with Mike Stay, Math. Struct. Comp. Sci. 22 (2012), 771787.

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

Quantum techniques
for studying equilibrium in chemical reaction networks, with
Brendan Fong, Journal of Complex Networks 3 (2014), 2234.

A Bayesian characterization
of relative entropy, with Tobias Fritz, Theory
and Applications of Categories 29 (2014), 421456.

G_{2} and the
rolling ball, with John Huerta, Trans. Amer. Math. Soc.
366 (2014), 52575293.

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

Quantropy,
with Blake S. Pollard,
Entropy 17 (2015), 772789.

Teleparallel gravity
as a higher gauge theory, with Derek Wise,
Comm. Math. Phys. 333 (2015), 153186.

Categories in control,
with Jason Erbele, Theory and
Applications of Categories 30 (2015), 836881.

The Lebesgue universal
covering problem, with Karine Bagdasaryan and Philip Gibbs,
Journal
of Computational Geometry 6 (2015), 288299.

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

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

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

Operads
and phylogenetic trees, with Nina Otter, Theory
and Applications of Categories 32 (2017), 13971453.

Props in
network theory, with Brandon Coya and Franciscus Rebro,
Theory and
Applications of Categories 33 (2018), 727783.

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

A compositional framework
for passive linear networks, with Brendan Fong, Theory and
Applications of Categories 33 (2018), 11581222.

Coarsegraining open
Markov processes, with Kenny Courser, Theory and
Applications of Categories 33 (2018), 12231268.

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

Open Petri nets, with
Jade Master, Mathematical
Structures in Computer Science 30 (2020), 314341.

Network models, with
John Foley, Blake S. Pollard and Joe Moeller, Theory and
Applications of Categories 35 (2020), 700744.

Enriched Lawvere theories
for operational semantics, with Christian Williams, proceedings
of Applied Category Theory 2019, Electronic
Proceedings of Theoretical Computer Science 323 (2020), 106135.

Structured cospans,
with Kenny Courser, Theory and
Applications of Categories 35 (2020), 17711822.

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. 281326.

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

Operads for designing systems of
systems, with John Foley, Notices
Amer. Math. Soc. 68 (2021), 10051007.

Categories of nets,
with Fabrizio Genovese, Jade Master and Michael Shulman, in
36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
IEEE, Rome, Italy, 2021, pp. 113.

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

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

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

Getting to the bottom of
Noether's theorem, in Philosophy and Physics of Noether's
Theorems: A Centenary Conference on the 1918 Work of Emmy Noether,
eds. Bryan W. Roberts and Nicholas Teh, Cambridge U. Press, Cambridge,
pp. 6699.

Compositional modeling with
stock and flow diagrams, with Xiaoyan Li, Sophie Libkind, Nathaniel
D. Osgood and Evan Patterson, Proceedings Fifth International Conference
on Applied Category Theory, EPTCS 380 (2022), 7796.

Compositional
thermostatics, with Owen Lynch and Joe Moeller,
Jour. Math. Phys. 64 (2023), 023304. (16 pages.)

A categorical framework
for modeling with stock and flow diagrams, with Xiaoyan Li, Sophie
Libkind, Nathaniel D. Osgood and Eric Redekopp, in Mathematics of
Public Health: Mathematical Modelling from the Next Generation,
eds. Jummy David and Jianhong Wu, Springer, 2023, pp. 175207.

Hoàng
Xuân Sính's thesis: categorifying group theory,
Thang Long Journal of Science: Mathematics and Mathematical Sciences
2 (2023), 135. Also in the book
Hoàng Xuân Sính's GrCatégories,
2023, pp. 1334.

Schur functors and
categorified plethysm, with Joe Moeller and Todd Trimble,
Higher Structures 8 (2024), 153.

Motivating motives. To appear in proceedings
of the Grothendieck Conference, Chapman University, May 2428, 2022.
(15 pages.)

Topological crystals.

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

Young diagrams
and classical groups. (19 pages.)
Popularizations

Social
structures that enable inventions,
in The Greatest Inventions of the Past 2000 Years, ed.
John Brockman, Simon and Schuster, 2000, pp. 6869.

The quantum of area?,
Nature 421 (2003), 702703.

The stringloop
war, in What Have You Changed Your Mind About?, ed. John
Brockman, Harper, 2009, pp. 156158.

The Earth — for physicists,
PhysicsWorld,
August 2009, 2226.

The strangest numbers in string
theory, with John Huerta, Scientific American, May 2011, 6065.
Also in The Best Writing on Mathematics 2012, ed. Mircea Pitici,
Princeton U. Press, Princeton, 2012, pp. 5060.

Monte Carlo methods in climate science,
with David Tweed, Math Horizons 21 (2013), 58.

From the icosahedron to
E_{8}, London Math. Soc.
Newsletter 476 (2018), 1823.

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.

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?)

Is
net zero emissions an impossible goal?, Nautilus, November
28, 2019.

The tenfold
way, Notices
Amer. Math. Soc. 67 (November 2020), 15991601.

This Week's Finds in
Mathematical Physics (1–50), 2021, 242 pages.

The joy of
condensed matter physics, Nautilus, February 25, 2021.

The Brownian map, Notices
Amer. Math. Soc. 68 (May 2021), 801803.

The
Gauss–Lucas theorem,
Notices Amer. Math. Soc. 68 (December 2021), 19881989.

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), 292296.

The Kuramoto–Sivashinsky
equation, with Steve Huntsman and Cheyne Weis,
Notices Amer. Math. Soc. 69 (October 2022), 15811583.

This Week's Finds in
Mathematical Physics (51–100), 2022, 281 pages.

Isbell duality,
Notices
Amer. Math. Soc. 70 (January 2023), 140141.

This Week's Finds in
Mathematical Physics (101–150), 2023, 347 pages.

The icosidodecahedron,
Notices Amer. Math. Soc. 70 (May 2023), 821823.

The beauty of roots, with J. Daniel Christensen
and Sam Derbyshire, Notices Amer. Math. Soc.,
70 (October 2023), 14951497.

The moduli space of acute
triangles,
Notices Amer. Math. Soc., 71 (May 2024), 664665.

Why mathematics is boring, to
appear in Notices Amer. Math. Soc.

The hexagonal tiling honeycomb,
to appear in Notices Amer. Math. Soc.
Book Reviews

The Physical Basis of the Direction of Time,
by H. D. Zeh, review in Math. Intelligencer 16 (1994), 7275.

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), 229243.

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

Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, edited by Joseph Kouneiher, review in Notices Amer. Math. Soc. 66 (November 2019), 16901692.
Theses

Recursivity in Quantum Mechanics, B.A thesis, advisor John Burgess,
Princeton University, May 1982.

Conformally Invariant Quantum Fields, Ph.D. thesis, advisor
Irving Segal, Massachusetts Institute of Technology, May 1986.
Of making books there is no end, and much study is a weariness
of the flesh...  Ecclesiastes 12:12
© 2021 John Baez
baez@math.removethis.ucr.andthis.edu