BRST analysis of general mechanical systems

TL;DR

This paper explores the BRST cohomology of general ordinary differential equations, revealing connections between symmetries, conservation laws, Lagrange structures, and quantization methods.

Contribution

It explicitly computes cohomology groups for non-Lagrangian systems and links Lagrange structures with weak Poisson brackets, extending quantization frameworks.

Findings

Identifies cohomology groups with physical significance

Shows isomorphism between Lagrange structures and weak Poisson brackets

Establishes a link between path-integral and deformation quantization

Abstract

We study the groups of local BRST cohomology associated to the general systems of ordinary differential equations, not necessarily Lagrangian or Hamiltonian. Starting with the involutive normal form of the equations, we explicitly compute certain cohomology groups having clear physical meaning. These include the groups of global symmetries, conservation laws and Lagrange structures. It is shown that the space of integrable Lagrange structures is naturally isomorphic to the space of weak Poisson brackets. The last fact allows one to establish a direct link between the path-integral quantization of general not necessarily variational dynamics by means of Lagrange structures and the deformation quantization of weak Poisson brackets.