Based on Polyakov's evaluation of the Fadeev-Popov determinant for (1+1)-dimensional gravity in the conformal gauge we formulate a canonical quantization in the synchronous gauge. We find that the system is describable as a quantum mechanical system of one degree of freedom. The quantization can be carried out and solved when any number of gauge fields are included. Scalar and spinor fields lead to new difficulties. For positive cosmological constant the geometry collapses as suggested by the classical system. For negative cosmological constant a more interesting behavior involving exponentially expanding and contracting universes occurs.
|Original language||English (US)|
|Number of pages||22|
|Journal||International Journal of Theoretical Physics|
|State||Published - May 1984|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)