Superfield Formulation of the Phase Space Path Integral

TL;DR

This paper develops a superfield formulation for the phase space path integral applicable to curved spaces and constrained systems, unifying transformations and ensuring correct measures through superpartners.

Contribution

It introduces a superfield approach that naturally incorporates canonical and BRST transformations, providing a first-principles derivation of the path integral measure for constrained systems.

Findings

Superfield formulation reproduces correct path integral measure.

Unifies canonical and BRST transformations in a single framework.

Applicable to curved phase spaces with various constraints.

Abstract

We give a superfield formulation of the path integral on an arbitrary curved phase space, with or without first class constraints. Canonical tranformations and BRST transformations enter in a unified manner. The superpartners of the original phase space variables precisely conspire to produce the correct path integral measure, as Pfaffian ghosts. When extended to the case of second-class constraints, the correct path integral measure is again reproduced after integrating over the superpartners. These results suggest that the superfield formulation is of first-principle nature.