Unexciting classical backgrounds

TL;DR

This paper investigates special time-dependent backgrounds in quantum field theory where no net particle production occurs, constructing explicit examples and exploring their limitations and open problems.

Contribution

It explicitly constructs all unexciting backgrounds for the harmonic oscillator and extends the concept to inhomogeneous field theories, highlighting the limitations and open questions.

Findings

All unexciting frequencies for the harmonic oscillator are explicitly constructed.

Homogeneous backgrounds with no particle production in any mode are identified.

Open problem: characterizing unexciting inhomogeneous backgrounds under physical interactions.

Abstract

Quantum fields in time-dependent backgrounds generally lead to particle production. Here we consider "unexciting" backgrounds for which the net particle production vanishes. We start by considering the simple harmonic oscillator and explicitly construct all unexciting time-dependent frequencies. This allows us to construct homogeneous backgrounds in field theory for which there is no particle production in any given mode, though we are able to show that there are no homogeneous backgrounds for which the particle production vanishes in every mode. We then construct general inhomogeneous unexciting field theory backgrounds. The set of all unexciting field theory backgrounds will be further restricted by the choice of physical interactions and this leads to an interesting open problem.