The Polymer representation for the scalar field: A Wigner functional approach

TL;DR

This paper explores the polymer representation of scalar fields using deformation quantization, deriving the Wigner functional as a limit of Gaussian measures, linking algebraic and Fock quantizations.

Contribution

It introduces a novel derivation of the polymer Wigner functional via deformation quantization, connecting it with algebraic and Fock methods.

Findings

Polymer Wigner functional obtained as Gaussian measure limit

Connection established between deformation and algebraic quantizations

Provides a unified framework for scalar field quantization

Abstract

In this paper, we analyze the polymer representation of the real-valued scalar field theory within the deformation quantization formalism. Specifically, we obtain the polymer Wigner functional by taking the limit of Gaussian measures in the Schodinger representation. The limiting functional corresponds to the polymer representation derived by using algebraic methods such as the GNS construction, and the Fock quantization procedure.