Magnetic Field and Curvature Effects on Pair Production I: Scalars and Spinors

Abstract

The pair production rates for spin-zero and spin-$\frac{1}{2}$ particles are calculated on spaces of the form $M \times {\mathbb R}^{1,1}$ with $M$ corresponding to ${\mathbb R}^2$ (flat), $T^2$ (flat, compactified), $S^2$ (positive curvature) and $H^2$ (negative curvature), with and without a background magnetic field on $M$. The motivation is to elucidate the effects of curvature and background magnetic field. Contrasting effects for positive and negative curvature on the two cases of spin are obtained. For positive curvature, we find enhancement for spin-zero and suppression for spin-$\frac{1}{2}$, with the opposite effect for negative curvature.