Two approaches to anomaly-free quantization of general covariant systems on an example of a two-dimensional string

TL;DR

This paper compares two methods for anomaly-free quantization of a two-dimensional string, one canonical and one involving mean value constraints, both avoiding indefinite metric states.

Contribution

It introduces and analyzes a novel weakening of Dirac quantization conditions for covariant systems, ensuring anomaly-free results without indefinite metrics.

Findings

Both approaches successfully avoid anomalies.

No states with indefinite metrics are present.

The mean value approach simplifies constraint solving.

Abstract

In this paper we discuss two approaches to anomaly-free quantization of a two-dimensional string. The first approach is based on the canonical Dirac prescription of quantization of degenerated systems. At the second approach we "weaken" the Dirac quantization conditions requiring the solving of first class constraints only in the sense of mean values. At both approaches there are no states with the indefinite metrics.