A Modular Invariant Quantum Theory From the Connection Formulation of (2+1)-Gravity on the Torus

Abstract

By choosing an unconventional polarization of the connection phase space in (2+1)-gravity on the torus, a modular invariant quantum theory is constructed. Unitary equivalence to the ADM-quantization is shown.

Latex, 4 pages

References in corpus (5)

• An algebraic extension of Dirac quantization: Examples
• (2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• Loop Representations for 2+1 Gravity on a Torus
• New Loop Representations for 2+1 Gravity

Cited by in corpus (3)

• Combinatorial quantisation of the Euclidean torus universe
• The Quantum Modular Group in (2+1)-Dimensional Gravity
• Diffeomorphism invariant subspaces in Witten's 2+1 quantum gravity on $\mathbf{R}\times T^2$