Unexciting classical backgrounds

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.

Automated summary

This article investigates quantum fields in time-dependent backgrounds and discovers certain backgrounds where particle production is zero. By studying the simple harmonic oscillator, the authors explicitly construct all unexciting time-dependent frequencies and create corresponding homogeneous backgrounds. However, there are no homogeneous backgrounds where particle production vanishes in every mode.