Higher-dimensional algebra - a language for quantum spacetime

Higher-dimensional algebra - a language for quantum spacetime

[John Baez]

Dear Categorists:

Some of you might like to see the transparencies of this talk:

http://math.ucr.edu/home/baez/quantum_spacetime/

It's a general colloquium talk, where I'll try to explain to the
physicists at the Perimeter Institute how higher categories show
up in physics.  You won't learn any category theory here.  If you
want details, there are links to some papers.

Best,
jb

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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.