Quantization of generally covariant systems with extrinsic time

TL;DR

This paper explores the quantization of generally covariant systems using extrinsic time, leveraging conformal Killing vectors and BRST formalism to construct consistent constraint operators.

Contribution

It introduces a method to deparametrize covariant systems with extrinsic time and constructs well-ordered constraint operators satisfying the algebra.

Findings

Constraint operators satisfying the algebra are explicitly constructed.

BRST formalism guides the search for these operators.

The approach applies to systems with conformal temporal Killing vectors.

Abstract

A generally covariant system can be deparametrized by means of an ``extrinsic'' time, provided that the metric has a conformal ``temporal'' Killing vector and the potential exhibits a suitable behavior with respect to it. The quantization of the system is performed by giving the well ordered constraint operators which satisfy the algebra. The searching of these operators is enlightned by the methods of the BRST formalism.