# Breaking of adiabatic invariance in the creation of particles by electromagnetic fields

## TL;DR

This paper investigates conditions under which the expected adiabatic invariance of particle number breaks down in electromagnetic fields, revealing a connection to the axial anomaly during particle creation from the vacuum.

## Contribution

It demonstrates the failure of adiabatic invariance in specific electromagnetic backgrounds and links this phenomenon to the axial anomaly, using a Sauter-type electric pulse as a model.

## Key findings

- Adiabatic invariance can break down in electromagnetic backgrounds.
- The breaking of invariance is related to the axial anomaly.
- Particle creation is influenced by electromagnetic field configurations.

## Abstract

Particles are spontaneously created from the vacuum by time-varying gravitational or electromagnetic backgrounds. It has been proven that the particle number operator in an expanding universe is an adiabatic invariant. In this paper we show that, in some special cases, the expected adiabatic invariance of the particle number fails in presence of electromagnetic backgrounds. In order to do this, we consider as a prototype a Sauter-type electric pulse. Furthermore, we also show a close relation between the breaking of the adiabatic invariance and the emergence of the axial anomaly.