The Quantization of Anomalous Gauge Field Theory and BRST-invariant Models of Two Dimensional Quantum Gravity

TL;DR

This paper generalizes the Faddeev-Shatashvili quantization method for anomalous gauge theories, demonstrating how classically equivalent theories can differ quantum mechanically while maintaining BRST invariance, with applications to 2D quantum gravity models.

Contribution

It introduces a generalized quantization approach for anomalous gauge theories that preserves BRST invariance and explores its implications for 2D quantum gravity models.

Findings

Classically equivalent theories can be quantum mechanically distinct.

The generalized method maintains BRST invariance despite anomalies.

Application to 2D induced gravity models shows new physically distinct theories.

Abstract

We analyze the problems with the so called gauge invariant quantization of the anomalous gauge field theories originary due to Faddeev and Shatashvili (FS). Our analysis bring to a generalization of FS method which allows to construct a series of classically equivalent theories which are non equivalent at quantum level. We prove that these classical theories are all consistent with the BRST invariance of the original gauge symmetry with suitably augmented field content. As an example of such a scenario, we discuss the class of physically distinct models of two dimensional induced gravity which are a generalization of the David-Distler-Kawai model.