#### John Baez

#### May 29, 1999

## Spin Networks, Spin Foams, and Quantum Gravity

A spin network is a graph with edges labeled by
representations of some group and vertices labeled by intertwining operators.
Thanks in part to the introduction of spin network techniques, we now have
a mathematically
rigorous and intuitively compelling picture of the kinematical aspects
of loop quantum gravity. Indeed, since spin networks form a convenient
basis of kinematical states, they have largely replaced collections of
loops as our basic model for 'quantum 3-geometries'. But to better understand
the dynamical aspects of quantum gravity, we would also like a model for
'quantum 4-geometries'. In other words, we want a truly quantum-mechanical
description of the geometry of spacetime. Recently the notion of 'spin
foam' has emerged as an interesting candidate. A spin foam is a 2-dimensional
cell complex with faces labeled by representations and edges labeled by
intertwining operators; generically, any slice of a spin foam gives a spin
network.

Click on these figures to see the slides.

For more on this subject try these papers:

© 1999 John Baez

baez@math.removethis.ucr.andthis.edu