Variational approximations for correlation functions in quantum field theories

TL;DR

This paper develops variational methods based on the Balian-Vénéroni principle to approximate multi-time correlation functions in quantum ^4 field theory, considering both Gaussian initial states and partial initial data, with explicit calculations at equilibrium.

Contribution

It introduces a variational approach for multi-time correlation functions in quantum field theory, including optimization over initial states, extending previous methods.

Findings

Explicit two-time correlation functions at equilibrium in the symmetric phase.

Comparison of initial state assumptions and their impact on correlation approximations.

Demonstration of the method's applicability to ^4 field theory.

Abstract

Applying the time-dependent variational principle of Balian and V\'en\'eroni, we derive variational approximations for multi-time correlation functions in $\Phi^4$ field theory. We assume first that the initial state is given and characterized by a density operator equal to a Gaussian density matrix. Then, we study the more realistic situation where only a few expectation values are given at the initial time and we perform an optimization with respect to the initial state. We calculate explicitly the two-time correlation functions with two and four field operators at equilibrium in the symmetric phase.