A novel approach to particle production in an uniform electric field

TL;DR

This paper introduces a new gauge-based method for describing scalar particle production in a uniform electric field, revealing similarities with Hawking radiation and highlighting previously overlooked boundary effects.

Contribution

It presents a novel lightcone gauge approach that differs from the standard harmonic oscillator paradigm, providing new insights into particle production mechanisms.

Findings

Effective Lagrangian matches standard results

Lightcone gauge modes can be explicitly normalized

Boundary factors affect Bogolubov coefficients in the uniform limit

Abstract

We outline a different method of describing scalar field particle production in a uniform electric field. In the standard approach, the (analytically continued) harmonic oscillator paradigm is important in describing particle production. However, there is another gauge in which the particle production process has striking similarities with the one used to describe Hawking radiation in black holes. The gauge we use to describe the electric field in is the lightcone gauge, so named because the mode functions for a scalar field are found to be singular on the lightcone. We use these modes in evaluating the effective Lagrangian using the proper time technique. The key feature of this analysis is that these modes can be explicitly "normalized" by using the criterion that they reduce to the usual flat space modes in the limit of the electric field tending to zero. We find that the proper time kernel is not the same as the analytically continued oscillator kernel though the effective Lagrangian is the standard result as it should be. We also consider an example of a confined electric field system using the lightcone gauge modes. Our analysis indicates that the Bogolubov coefficients, in taking the limit to the uniform electric field case, are multiplied by energy dependent boundary factors that have not been taken into account before.