Master equation in the general gauge: on the problem of infinite reducibility

TL;DR

This paper discusses the quantization of the master equation in a general gauge, highlighting issues of infinite reducibility and the unique approach of using coupled functional integrals without ghosts.

Contribution

It introduces a novel quantization method for gauge theories with nilpotent generators that avoids ghosts and addresses the problem of infinite reducibility.

Findings

Quantization involves coupled functional integrals and square roots.

In special gauges, integrals decouple and simplify.

The approach handles infinite reducibility in gauge theories.

Abstract

The master equation is quantized. This is an example of quantization of a gauge theory with nilpotent generators. No ghosts are needed for a generation of the gauge algebra. The point about the nilpotent generators is that one can't write down a single functional integral for this theory. One has to write down a product of two coupled functional integrals and take a square root. In the special gauge where the gauge conditions are commuting, the functional integrals decouple, and one recovers the known result.