Vacuum Pair Creation in Spin Noncommutative of Coordinates: Volkov Background and Constant Electric Field

TL;DR

This paper explores how spin noncommutativity of coordinates affects vacuum pair creation in strong electromagnetic fields, finding that it can enhance or suppress pair production depending on the background, with a critical deformation parameter causing divergence.

Contribution

It introduces a novel analysis of vacuum pair creation under spin noncommutative geometry, deriving explicit formulas and revealing critical behavior in strong-field QED.

Findings

Pair creation probability is zero in Volkov background even with spin noncommutativity.

Constant electric field sees enhanced pair creation due to spin noncommutativity.

Divergence at critical deformation parameter indicates potential vacuum instability.

Abstract

We investigate the phenomenon of vacuum pair creation for Dirac fermions subjected to a Volkov plane wave and a constant electric field within the framework of spin noncommutativity of coordinates. Employing the Schwinger proper-time formalism, we derive the effective action and obtain closed-form expressions for the pair creation probability. Our analysis reveals that, in the presence of a Volkov plane wave background, the pair production probability remains zero-even with spin noncommutativity. In contrast, for a constant electric field in $(1+1)$-dimensional spacetime, the spin-induced noncommutative deformation significantly enhances the pair creation probability. Remarkably, we identify a critical value of the deformation parameter, $\ell = \frac{m}{eE}$, at which the pair creation probability diverges, indicating a potential vacuum instability or a breakdown of the perturbative regime. These findings underscore the nontrivial role of spin noncommutativity in nonperturbative quantum electrodynamics and offer novel insights for future studies in strong-field physics.