Action Principle and Modification of the Faddeev-Popov Factor in Gauge Theories

TL;DR

This paper uses the quantum action principle to analyze the Faddeev-Popov factor in gauge theories, revealing that modifications are needed in more general cases and that gauge invariance does not always guarantee the standard FP factor.

Contribution

It demonstrates the necessity to modify the Faddeev-Popov factor in certain gauge theories and derives expressions for these modifications without relying on path integral methods.

Findings

The Faddeev-Popov factor requires modification in non-standard gauge theories.

Gauge invariance does not necessarily imply the standard FP factor.

Derived explicit expressions for modified FP factors.

Abstract

The quantum action (dynamical) principle is exploited to investigate the nature and origin of the Faddeev-Popov (FP) factor in gauge theories without recourse to path integrals. Gauge invariant as well as gauge non-invariant interactions are considered to show that the FP factor needs to be modified in more general cases and expressions for these modifications are derived. In particular we show that a gauge invariant theory does not necessarily imply the familiar FP factor for proper quantization.