John Baez

Lecture at the Minnowbrook Symposium on Space-Time Structure

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.

foam01.jpg foam02.jpg foam03.jpg foam04.jpg foam05.jpg foam.jpg foam07.jpg foam08.jpg foam09.jpg foam10.jpg foam11.jpg foam12.jpg foam13.jpg


For more on this subject try these papers:


© 1999 John Baez
baez@math.removethis.ucr.andthis.edu

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