Deformation Quantization of Classical Fields

TL;DR

This paper explores the deformation quantization of classical scalar and abelian gauge fields, deriving star-products and Wigner functionals, and analyzing effects of topology within this formalism.

Contribution

It provides explicit constructions of quantization tools for classical fields and examines the impact of topology on deformation quantization.

Findings

Wigner functionals are factorized into physical and constraint parts for abelian gauge theories

Explicit star-products and Wigner functionals are derived for scalar and gauge fields

Topology influences the structure of deformation quantization in field theories

Abstract

We study the deformation quantization of scalar and abelian gauge classical free fields. Stratonovich-Weyl quantizer, star-products and Wigner functionals are obtained in field and oscillator variables. Abelian gauge theory is particularly intriguing since Wigner functional is factorized into a physical part and other one containing the constraints only. Some effects of non-trivial topology within deformation quantization formalism are also considered.