Exact Dirac Quantization of All 2-D Dilaton Gravity Theories

TL;DR

This paper performs an exact Dirac quantization of the most general 2D dilaton gravity theories, explicitly constructing the reduced phase space and solving the quantum constraints to obtain invariant wave functionals.

Contribution

It provides a complete Hamiltonian analysis and exact quantum solutions for all 2D dilaton gravity theories within a unified framework.

Findings

Explicit construction of the two-dimensional reduced phase space.

Exact solutions to quantum constraints for all considered theories.

Wave functionals depend on configuration space and spacetime embedding.

Abstract

The most general dilaton gravity theory in 2 spacetime dimensions is considered. A Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the fields. The theory is then quantized via the Dirac method in a functional Schrodinger representation. The quantum constraints are solved exactly to yield the (spatial) diffeomorphism invariant quantum wave functional for all theories considered. This wave function depends explicitly on the (single) configuration space coordinate as well as on the imbedding of space into spacetime (i.e. on the choice of time).