John Baez
May 31, 2006
HigherDimensional Algebra: A Language for Quantum Spacetime
Category theory is a general language for describing things
and processes  called "objects" and "morphisms".
In this language, the counterintuitive features of quantum theory turn
out to be properties that the category of Hilbert spaces shares
with the category of cobordisms  in which objects are choices
of "space", and morphisms are choices of "spacetime". The
striking similarities between these categories suggests that
"ncategories with duals" are a promising framework for a
quantum theory of spacetime. We sketch the historical development
of these ideas from Feynman diagrams, to string theory,
topological quantum field theory, spin networks and spin foams,
and especially recent work on openclosed string theory, quantum
gravity coupled to point particles, and 4d BF theory coupled to
strings.

You can see the transparencies for this talk
in PDF and Postscript

You can also see a
video of this talk.
If you have trouble, go here,
click on "Seminar Series", and search under my name.
Experts will note that I say the cobordism group is nontrivial
in 3 dimensions; I should have said 4 dimensions! Nonexperts
will enjoy the thunderstorm that repeatedly knocks out the
overhead projector.
For more on this subject try these introductory papers:
Also try these somewhat more technical ones:

Samson Abramsky and Bob Coecke,
A Categorical Semantics of Quantum Protocols

John Baez,
An Introduction to Spin
Foam Models of BF Theory and Quantum Gravity

John Baez, Alissa Crans and Derek Wise,
Exotic Statistics
for Strings in 4d BF Theory

John Baez and Alejandro Perez,
Quantization of
Strings and Branes Coupled to BF Theory

John Baez and Urs Schreiber, Higher
Gauge Theory

Laurent Freidel and David Louapre,
PonzanoRegge
Model Revisited I: Gauge Fixing, Observables and Interacting
Spinning Particles

Laurent Freidel and David Louapre,
PonzanoRegge
Revisited II: Equivalence with ChernSimons

Aaron Lauda and Hendryk Pfeiffer,
OpenClosed Strings:
TwoDimensional Extended TQFTs and Frobenius Algebras

Aaron Lauda and Hendryk Pfeiffer,
State Sum Construction of TwoDimensional OpenClosed Topological
Quantum Field Theories

Karin Noui and Alejandro Perez,
Three
Dimensional Loop Quantum Gravity: Coupling to Point Particles

Ingo Runkel, Jürgen Fuchs and Christoph Schweigert,
Categorification
and Correlation Functions in Conformal Field Theory

Ingo Runkel, Jens Fjelstad, Jürgen Fuchs and Christoph Schweigert,
Topological
and Conformal Field Theory and Frobenius Algebras

Urs Schreiber,
From Loop Space Mechanics to Nonabelian Strings
Text © 2006 John Baez
Images © Aaron Lauda (top) and Derek Wise (bottom)
baez@math.removethis.ucr.andthis.edu