BRST theory without Hamiltonian and Lagrangian

TL;DR

This paper develops a BRST formulation applicable to generic gauge systems without relying on Hamiltonian or Lagrangian structures, enabling deformation quantization via Kontsevich's theorem and unifying existing schemes.

Contribution

It introduces a universal BRST framework for gauge systems lacking Hamiltonian or Lagrangian structures, extending quantization methods to broader contexts.

Findings

Constructed a consistent BRST formulation for generic gauge systems.

Demonstrated deformation quantization using Kontsevich's formality theorem.

Connected the framework to sigma-model interpretations.

Abstract

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.