Quantum localization of Classical Mechanics

TL;DR

This paper explores how specific gauge choices in BRST-BFV and BV quantization methods lead to quantum localization phenomena in classical mechanics, connecting gauge fixing to localization in path integrals.

Contribution

It demonstrates that particular gauge fixing functions and solutions to the classical master equation induce Hamiltonian and Lagrangian localization in the path integral formulations.

Findings

Hamiltonian localization achieved via special gauge fixing and unitary limit.

Lagrangian localization obtained through extremals and solutions to the classical master equation.

Provides a link between gauge choices and localization phenomena in quantized classical systems.

Abstract

Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.