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

TL;DR

This paper develops a modular invariant quantum theory for (2+1)-gravity on the torus by selecting an unconventional polarization, demonstrating its unitary equivalence to the ADM-quantization.

Contribution

It introduces a novel polarization approach in connection phase space, leading to a modular invariant quantum formulation of (2+1)-gravity.

Findings

Constructed a modular invariant quantum theory.

Proved unitary equivalence to ADM-quantization.

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.