Wigner Functional Approach to Quantum Field Dynamics

TL;DR

This paper introduces the Wigner functional for quantum fields, linking classical solutions to quantum dynamics, and explores its applications in thermodynamics and phase transitions.

Contribution

It presents a novel Wigner functional framework for quantum fields and discusses methods for its numerical evaluation and applications in phase transition analysis.

Findings

Explicit solution for the Wigner functional during the 'roll-over' phase transition

Connection between classical field equations and quantum evolution

Discussion of approximate numerical methods for the Wigner functional

Abstract

We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical field equations to the time evolution of the quantum field. We discuss the field in thermodynamical equilibrium and find the explicit solution of the equations of motion for the so-called ``roll-over'' phase transition. Finally, we briefly discuss the approximate methods for the evaluation of the Wigner functional that may be used to numerically simulate the initial value problem..