Subject: categories: higher-dimensional algebra and Planck-scale physics

From: john baez <[email-masked]>
Date: Fri, 5 Feb 1999 17:26:13 -0800 (PST)

Here is a new paper of mine that may be interesting to fans of
categories and n-categories:

Higher-Dimensional Algebra and Planck-Scale Physics

to appear in "Physics Meets Philosophy at the Planck Scale", eds. 
Craig Callender and Nick Huggett, Cambridge U. Press, Cambridge.

This is a nontechnical introduction to recent work on quantum gravity
that uses ideas from higher-dimensional algebra.  We argue that reconciling
general relativity with the Standard Model requires a `background-free
quantum theory with local degrees of freedom propagating causally'.  We
describe the insights provided by work on topological quantum field theories
such as quantum gravity in 3-dimensional spacetime.  These are background-free
quantum theories lacking local degrees of freedom, so they only display some
of the features we seek.  However, they suggest a deep link between the
concepts of `space' and `state', and similarly those of `spacetime' and
`process', which we argue is to be expected in any background-free quantum
theory.  We sketch how higher-dimensional algebra provides the mathematical
tools to make this link precise.  Finally, we comment on attempts to formulate
a theory of quantum gravity in 4-dimensional spacetime using `spin networks'
and `spin foams'.

Available in LaTeX and Postscript form at

http://xxx.lanl.gov/abs/gr-qc/9902017

and in Postscript form at

http://math.ucr.edu/home/baez/planck.ps