John Baez

Colloquium at the Perimeter Institute

May 31, 2006

Higher-Dimensional 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 "n-categories 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 open-closed string theory, quantum gravity coupled to point particles, and 4d BF theory coupled to strings.

For more on this subject try these introductory papers:

Also try these somewhat more technical ones:

Text © 2006 John Baez
Images © Aaron Lauda (top) and Derek Wise (bottom)