Real-time Quantum evolution in the Classical approximation and beyond

TL;DR

This paper introduces a method based on the Wigner function to systematically incorporate quantum corrections into real-time evolution calculations in quantum field theory, extending classical approximations.

Contribution

It proposes a new approach for computing quantum corrections to classical evolution using the Wigner function, applicable to quantum field theory.

Findings

The method provides systematic quantum corrections to expectation values.

Comparison shows good agreement with exact quantum results for few degrees of freedom.

Numerical effort scales favorably with the number of variables.

Abstract

With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural way to justify and extend the classical approximation. A simple proposal is presented that can allow to give systematic quantum corrections to the evolution of expectation values and/or an estimate of the errors committed when using the classical approximation. The method is applied to the case of a few degrees of freedom and compared with other methods and with the exact quantum results. An analysis of the dependence of the numerical effort involved as a function of the number of variables is given, which allow us to be optimistic about its applicability in a quantum field theoretical context.