On the quantum BRST structure of classical mechanics

TL;DR

This paper extends the BRST-antiBRST invariant path integral approach from classical mechanics to pseudomechanics, revealing how physical propagators can be obtained through specific boundary conditions and connecting the formalism to group theory and Poisson brackets.

Contribution

It generalizes the BRST-antiBRST path integral formulation to pseudomechanics and links the natural bracket to the Poisson bracket, providing new insights into the operator formalism.

Findings

Projections to physical propagators via BRST-antiBRST boundary conditions.

Equivalence of the natural bracket to the Poisson bracket.

Insights into the operator formulation of the theory.

Abstract

The BRST-antiBRST invariant path integral formulation of classical mechanics of Gozzi et al is generalized to pseudomechanics. It is shown that projections to physical propagators may be obtained by BRST-antiBRST invariant boundary conditions. The formulation is also viewed from recent group theoretical results within BRST-antiBRST invariant theories. A natural bracket expressed in terms of BRST and antiBRST charges in the extended formulation is shown to be equal to the Poisson bracket. Several remarks on the operator formulation are made.