On quantization in background scalar fields

TL;DR

This paper investigates quantum effects and backreaction in scalar background fields within Yukawa theory in (0+1) and (1+1) dimensions, using exact solutions, classical backgrounds, and loop corrections.

Contribution

It provides exact solutions in (0+1) dimensions and analyzes quantum backreaction and loop corrections in (1+1) dimensions with specific scalar backgrounds.

Findings

Exact solutions in (0+1) dimensions.

Analysis of backreaction in scalar backgrounds.

Calculation of loop corrections using Schwinger--Keldysh technique.

Abstract

We consider (0+1) and (1+1) dimensional Yukawa theory in various scalar field backgrounds, which are solving classical equations of motion: $\ddot{\phi}_{cl} = 0$ or $\Box \phi_{cl} = 0$, correspondingly. The (0+1)--dimensional theory we solve exactly. In (1+1)--dimensions we consider background fields of the form $\phi_{cl} = E\, t$ and $\phi_{cl} = E\, x$, 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.