(2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root

Abstract

For (2+1)-dimensional spacetimes with the spatial topology of a torus, the transformation between the Chern-Simons and ADM versions of quantum gravity is constructed explicitly, and the wave functions are compared. It is shown that Chern-Simons wave functions correspond to modular forms of weight 1/2, that is, spinors on the ADM moduli space, and that their evolution (in York's ``extrinsic time'' variable) is described by a Dirac equation. (This version replaces paper 9109006, which was garbled by my mailer.)