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

TL;DR

This paper studies vacuum pair creation for Dirac fermions in strong external fields under spin noncommutative coordinates. Using the Schwinger proper-time formalism, it derives the modified effective action and propagators, revealing that a Volkov plane wave background does not induce pair production even with spin noncommutativity. In contrast, a (1+1)D constant electric field experiences enhanced Schwinger-like pair creation, with a critical deformation parameter $\ell_{\mathrm{crit}}=m/|eE|$ at which the vacuum becomes unstable and the production probability diverges. These results demonstrate a nontrivial role for spin noncommutativity in nonperturbative QED and suggest new avenues for exploring strong-field vacuum phenomena in extended spacetime frameworks.

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.

Figures (1)

• Figure 1: Dependence of the pair creation probability $\mathcal{P}$ on the electric field strength $\vert eE\vert$ and the spin noncommutativity parameter $\ell$.