Resonant particle creation by a time-dependent potential in a nonlocal theory

TL;DR

This paper analytically studies particle creation in a local scalar quantum theory with a time-dependent potential and explores how nonlocality in an infinite-derivative model causes resonant amplification of specific modes, affecting particle spectra.

Contribution

It provides an exact analytical calculation of particle creation in a local model and extends the analysis to a nonlocal theory, revealing resonance effects due to nonlocality.

Findings

Nonlocality causes resonant amplification of certain modes.

Particle spectrum is significantly affected by nonlocal effects.

Total number density of created particles increases due to resonance.

Abstract

Considering an exactly solvable local quantum theory of a scalar field interacting with a $\delta$-shaped time-dependent potential we calculate the Bogoliubov coefficients analytically and determine the spectrum of created particles. We then show how these considerations, when suitably generalized to a specific nonlocal "infinite-derivative" quantum theory, are impacted by the presence of nonlocality. In this model, nonlocality leads to a significant resonant amplification of certain modes, leaving its imprint not only in the particle spectrum but also in the total number density of created particles.