Exactly solvable cases in QED with t-electric potential steps

TL;DR

This paper provides detailed calculations of particle creation in exactly solvable time-dependent electric fields in QED, revealing universal behaviors and new results in modified and limiting cases of these fields.

Contribution

It introduces new calculations and insights into particle creation effects in exactly solvable electric field configurations, extending previous studies and deriving general conclusions.

Findings

New results in modified electric field configurations

Universal behavior of vacuum mean values in slowly varying fields

Detailed analysis of limiting cases in known solvable models

Abstract

In this paper, we present in detail consistent QED (and scalar QED) calculations of particle creation effects in external electromagnetic field that correspond to three most important exactly solvable cases of t-electric potential steps: Sauter-like electric field, T-constant electric field, and exponentially growing and decaying electric fields. In all these cases, we succeeded to obtain new results, such as calculations in modified configurations of the above mentioned steps and detailed considerations of new limiting cases in already studied before steps. As was recently discovered by us, the information derived from considerations of exactly solvable cases allows one to make some general conclusions about quantum effects in fields for which no closed form solutions of the Dirac (or Klein-Gordon) equation are known. In the present article we briefly represent such conclusions about an universal behavior of vacuum mean values in slowly varying strong electric fields.