Dirac's work on spinors has had a great impact throughout mathematics and physics. His work on "extensors" is far less well-known, but also interesting. Here we focus on the applications of these ideas to quantum gravity. In loop quantum gravity, the gravitational field is described in terms of its effect on the parallel transport of spin-1/2 test particles, leading to a formalism in which the quantum geometry of space is described using "spin networks". This theory makes specific predictions concerning the discreteness of geometrical observables such as area and volume, and gives an interesting picture of the microstates of a black hole. However, to address questions of dynamics, we also need a picture of the quantum geometry of spacetime. Recently the notion of "spin foam" has emerged as a interesting candidate, in which extensors may play an important role.

Click on this to see the slides as a PDF file:

Thanks go to Derek Wise for scanning in these slides.

For more on this subject try these papers:

- Loop Quantum Gravity by Carlo Rovelli
- Spin Foam Models by John Baez
- An Introduction to Spin Foam Models of BF Theory and Quantum Gravity by John Baez
- Integrability for Relativistic Spin Networks by John Baez and John Barrett
- Spin Foam Models of Riemannian Quantum Gravity by John Baez, J. Daniel Christensen, Thomas Halford and David Tsang
- Asymptotics of 10j Symbols by John Baez, J. Daniel Christensen and Greg Egan

© 2002 John Baez

baez@math.removethis.ucr.andthis.edu