Integrating Geometry in General 2D Dilaton Gravity with Matter

TL;DR

This paper develops a method to quantize 2D dilaton gravity with matter by using a path integral approach in a specific gauge, deriving the generating functional and effective interactions for scalar fields.

Contribution

It introduces a systematic perturbation theory for matter in 2D dilaton gravity within a specific gauge, deriving the generating functional and effective vertices.

Findings

Derived the general form of the generating functional.

Established the relation to classical solutions.

Calculated the effective 4-vertex for scalar fields.

Abstract

General 2d dilaton theories, containing spherically symmetric gravity and hence the Schwarzschild black hole as a special case, are quantized by an exact path integral of their geometric (Cartan-) variables. Matter, represented by minimally coupled massless scalar fields is treated in terms of a systematic perturbation theory. The crucial prerequisite for our approach is the use of a temporal gauge for the spin connection and for light cone components of the zweibeine which amounts to an Eddington Finkelstein gauge for the metric. We derive the generating functional in its most general form which allows a perturbation theory in the scalar fields. The relation of the zero order functional to the classical solution is established. As an example we derive the effective (gravitationally) induced 4-vertex for scalar fields.