Phase-space Quantization of Field Theory

TL;DR

This paper introduces a phase-space approach to quantum field theory using Wigner functionals, emphasizing gauge invariance and classical trajectories in simple cases, providing a pedagogical reformulation of scalar field theory.

Contribution

It presents a novel phase-space formulation of scalar field theory using Wigner functionals, highlighting gauge invariance and classical trajectories within a pedagogical framework.

Findings

Exact trajectories for the Wigner distribution are classical for simple harmonic oscillators.

Scalar field theory can be reformulated in terms of distributions in field phase-space.

The approach offers a pedagogical perspective on gauge invariance in phase-space.

Abstract

In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple - indeed, classical - for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published in J Phys A32 (1999) 771 and Phys Rev D58 (1998) 025002, reported at the Yukawa Institute Workshop "Gauge Theory and Integrable Models", 26-29 January, 1999.