Wigner Trajectory Characteristics in Phase Space and Field Theory

TL;DR

This paper derives exact classical-like trajectories for the Wigner phase-space distribution, reformulating scalar field theory in phase space and exploring applications to duality transformations.

Contribution

It introduces a Wigner functional formulation for scalar field theory based on explicit phase-space trajectories, bridging quantum and classical descriptions.

Findings

Exact trajectories for Wigner distribution in simple harmonic oscillator

Reformulation of scalar field theory in phase space

Discussion of duality transformations in field theory

Abstract

Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which 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. Applications to duality transformations in field theory are discussed.