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.

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For more on this subject try these papers:

© 1999 John Baez