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arXiv · hep-th/9109006

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

Steven Carlip
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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.)

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Steven Carlip. 1991-09-16. (2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root. https://doi.org/10.1103/physrevd.45.3584%2010.1103%2Fphysrevd.47.1729

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