Quantization in background scalar fields

Abstract

We consider (0+1) and (1+1) dimensional Yukawa theory in various scalar field backgrounds, which are solving classical equations of motion: φcl=0 or □φcl=0, correspondingly. The (0+1)-dimensional theory we solve exactly. In (1+1)-dimensions we consider background fields of the form φcl=Et and φcl=Ex, which are inspired by the constant electric field. Here E is a constant. We study the backreaction problem by various methods, including the dynamics of a coherent state. We also calculate loop corrections to the correlation functions in the theory using the Schwinger-Keldysh diagrammatic technique.