Pair production of Dirac particles in a d+1-dimensional noncommutative space-time

TL;DR

This paper calculates the probability of Dirac fermion pair production in a (d+1)-dimensional noncommutative space-time using Seiberg-Witten maps, considering various electric field configurations.

Contribution

It introduces a method to compute pair production probabilities in noncommutative space-time using first-order Seiberg-Witten maps, extending previous work to higher dimensions and different field types.

Findings

Derived probability density formulas for pair production

Analyzed effects of constant and time-dependent electric fields

Extended calculations to (d+1)-dimensional noncommutative space

Abstract

This work addresses the computation of the propability of fermionic particle pair production in $(d+1)-$ dimensional noncommutative Moyal space. Using the Seiberg-Witten maps that establish relations between noncommutative and commutative field variables, to first order in the noncommutative parameter $\theta$, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent and space-dependent electric fields are considered and discussed.