Does a non-zero tunnelling probability imply particle production in time independent classical electromagnetic backgrounds?

TL;DR

This paper investigates whether non-zero tunnelling probabilities in quantum models of electromagnetic backgrounds truly indicate particle production, finding inconsistencies that challenge the tunnelling interpretation.

Contribution

The study critically examines the tunnelling interpretation in particle production, revealing inconsistencies between different theoretical approaches in time-independent magnetic fields.

Findings

Imaginary part of the effective Lagrangian is zero in magnetic fields, indicating no particle production.

Non-zero tunnelling probability exists in mode decomposition, suggesting possible particle production.

The inconsistency questions the validity of tunnelling probability as an indicator of particle creation.

Abstract

In this paper, we probe the validity of the tunnelling interpretation that is usually called forth in literature to explain the phenomenon of particle production by time independent classical electromagnetic backgrounds. We show that the imaginary part of the effective lagrangian is zero for a complex scalar field quantized in a time independent, but otherwise arbitrary, magnetic field. This result implies that no pair creation takes place in such a background. But we find that when the quantum field is decomposed into its normal modes in the presence of a spatially confined and time independent magnetic field, there exists a non-zero tunnelling probability for the effective Schr{\" o}dinger equation. According to the tunnelling interpretation, this result would imply that spatially confined magnetic fields can produce particles, thereby contradicting the result obtained from the effective lagrangian. This lack of consistency between these two approaches calls into question the validity of attributing a non-zero tunnelling probability for the effective Schr{\" o}dinger equation to the production of particles by the time independent electromagnetic backgrounds. The implications of our analysis are discussed.