Polymer quantization of CGHS model- I

TL;DR

This paper develops a loop quantum gravity approach to the two-dimensional CGHS dilatonic gravity model, constructing a quantum theory with a well-defined Hilbert space, spectrum, and deformed observable algebra, revealing quantum geometric effects.

Contribution

It introduces a polymer quantization of the CGHS model, including the construction of the physical Hilbert space and the quantization of Dirac observables with a deformed algebra.

Findings

Complete spectrum obtained via group averaging.

Unitary representation of spacetime diffeomorphisms.

Quantum deformation of the Dirac observable algebra.

Abstract

We present a polymer(loop) quantization of a two dimensional theory of dilatonic gravity known as the CGHS model. We recast the theory as a parametrized free field theory on a flat 2-dimensional spacetime and quantize the resulting phase space using techniques of loop quantization. The resulting (kinematical) Hilbert space admits a unitary representation of the spacetime diffeomorphism group. We obtain the complete spectrum of the theory using a technique known as group averaging and perform quantization of Dirac observables on the resulting Hilbert space. We argue that the algebra of Dirac observables gets deformed in the quantum theory. Combining the ideas from parametrized field theory with certain relational observables, evolution is defined in the quantum theory in the Heisenberg picture. Finally the dilaton field is quantized on the physical Hilbert space which carries information about quantum geometry.