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

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, $\mathrm{\ell }=\frac{m}{eE}$, 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.