One of the great challenges facing physics today is to reconcile quantum theory and general relativity. Loop quantum gravity is an approach to this challenge that incorporates quantum theory into our description of spacetime from the very start. Quantum states of the geometry of space are described by "spin networks" - graphs with certain labellings of their edges and vertices. The theory predicts that geometrical quantities such as area and volume take on a discrete spectrum of possible values, and it explains the entropy of black holes by associating information to each point at which a spin network edge punctures the event horizon. This is a nontechnical introduction to these ideas, focussing on some computational challenges that arise in studying this theory.

- Loop Quantum Gravity - in PDF or Postscript.

For more on this subject, start with these less technical papers:

- Carlo Rovelli, Loop Quantum Gravity.
- Abhay Ashtekar, Gravity and the Quantum.

Dig deeper with Carlo Rovelli's book, which is also available online:

- Carlo Rovelli, Quantum Gravity, Cambridge U. Press, 2004.

Then, for more specifics on things mentioned in my talk, try these:

- Marcin Domagala and Jerzy Lewandowski, Black Hole Entropy from Quantum Geometry.
- John Baez, An Introduction to Spin Foam Models of BF Theory and Quantum Gravity.
- Alejandro Perez, Introduction to Loop Quantum Gravity and Spin Foams.
- Daniele Oriti, Spin Foam Models of Quantum Spacetime.
- J. Daniel Christensen and Greg Egan, An Efficient Algorithm for the Riemannian 10j Symbols.
- John Baez, J. Daniel Christensen, Thomas Halford and David Tsang, Spin Foam Models of Riemannian Quantum Gravity.
- John Baez, J. Daniel Christensen and Greg Egan, Asymptotics of 10j Symbols.

- J. Daniel Christensen, Spin Networks, Spin Foams and Loop Quantum Gravity.

© 2005 John Baez

baez@math.removethis.ucr.andthis.edu