Out of equilibrium two-dimensional Yukawa theory in a strong scalar wave background

TL;DR

This paper investigates the non-equilibrium behavior of 2D Yukawa theory in a strong scalar wave background using operator and functional formalisms, revealing differences in propagators and physical quantities like fermion flux.

Contribution

It compares operator and functional formalisms in 2D Yukawa theory, highlighting differences in propagators and physical predictions in a strong scalar wave background.

Findings

Keldysh propagators differ between formalisms

Fermion stress energy flux varies between formalisms

Scalar current is consistent across formalisms for large, slow background

Abstract

We consider 2D Yukawa theory in the strong scalar wave background. We use operator and functional formalisms. In the latter the Schwinger--Keldysh diagrammatic technique is used to calculate retarded, advanced and Keldysh propagators. We use simplest states in the two formalisms in question, which appear to be different from each other. As the result two Keldysh propagators found in different formalisms do not coincide, while the retarded and advanced ones do coincide. We use these propagators to calculate physical quantities. Such as the fermion stress energy flux and the scalar current. The latter one is necessary to know to address the backreaction problem. It happens that while in the functional formalism (for the corresponding simplest state) we find zero fermion flux, in the operator formalism (for the corresponding simplest state) the flux is not zero and is proportional to a Schwarzian derivative. Meanwhile the scalar current is the same in both formalisms, if the background field is large and slowly changing.