Electron-positron pair creation in a vacuum by an electromagnetic field in 3+1 and lower dimensions

TL;DR

This paper calculates the probability of electron-positron pair creation in vacuum under external electromagnetic fields across 3+1, 2+1, and 1+1 dimensions, extending understanding of quantum field effects in various spacetime frameworks.

Contribution

It provides a comprehensive analysis of pair creation probabilities in different dimensional settings with arbitrary external electromagnetic fields, expanding previous studies limited to specific configurations.

Findings

Derived formulas for pair creation probabilities in 3+1 dimensions with arbitrary fields.

Extended analysis to 2+1 and 1+1 dimensions with similar results.

Demonstrated the dependence of pair creation on field magnitudes and directions.

Abstract

We calculate the probability of electron-positron pair creation in vacuum in 3+1 dimensions by an external electromagnetic field composed of a constant uniform electric field and a constant uniform magnetic field, both of arbitrary magnitudes and directions. The same problem is also studied in 2+1 and 1+1 dimensions in appropriate external fields and similar results are obtained.