##
3
Quantum Gravity in 2+1 Dimensions

The reader may well have decided that for an author reviewing
quantum gravity, I have spent an inordinate amount of time on the
classical theory. There is a good reason for this, though: Each
of the approaches described in the preceding sections leads very
naturally to an approach to quantization, which is now - with a
few twists - fairly straightforward. Indeed, the main reason that
2+1 dimensions offer such an attractive setting for quantum
gravity is that the classical solutions can be completely
described by a finite set of parameters. Such a description
effectively reduces quantum gravity to quantum mechanics,
allowing us to evade the complications of quantum field theory.
This is not to imply that all approaches to quantum gravity
simplify - the Wheeler-DeWitt equation, for example, apparently
does not - but it allows us to explore at least a few approaches
in depth.