Exact Operator Quantization of a Model of Two-Dimensional Dilaton Gravity

TL;DR

This paper presents an exact operator quantization of a two-dimensional dilaton gravity model, achieving a conformally invariant quantum theory with a complete set of physical states using BRST formalism.

Contribution

It introduces a non-linear, non-local quantum canonical transformation to quantize the model exactly, considering boundary conditions and conformal invariance.

Findings

Successfully quantized the model with 24 matter scalars

Achieved a conformally invariant quantum theory

Constructed the physical state space using BRST formalism

Abstract

Exact operator quantization is perfomed of a model of two-dimensional dilaton gravity in Lorentzian spacetime, classically equivalent to the one proposed by Callan, Giddings, Harvey and Strominger, in the special case with 24 massless matter scalars. This is accomplished by developing a non-linear and non-local quantum canonical transformation of basic interacting fields into a set of free fields, rigorously taking into account the spatially closed boundary condition. The quantized model enjoys conformal invariance and the entire set of physical states and operators are obtained in the BRST formalism. In addition, a rather detailed discussion of the nature of the basic issues for exact treatment of models of quantum gravity is provided.