On The Reduced Canonical Quantization Of The Induced 2D-Gravity

TL;DR

This paper compares three methods of quantizing induced 2D gravity on a compact spatial section, analyzing their differences and establishing an isomorphism between the resulting Hilbert spaces.

Contribution

It introduces and compares three approaches to quantize 2D gravity, highlighting their equivalences and differences in handling the Hamiltonian constraint.

Findings

Supermomentum constraint solved classically in all approaches

Different methods of imposing the Hamiltonian constraint analyzed

Established isomorphism between the Hilbert spaces of the approaches

Abstract

The quantization of the induced 2d-gravity on a compact spatial section is carried out in three different ways. In the three approaches the supermomentum constraint is solved at the classical level but they differ in the way the hamiltonian constraint is imposed. We compare these approaches establishing an isomorphism between the resulting Hilbert spaces.