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

## TL;DR

This paper investigates how magnetic fields and space curvature influence pair production rates for scalar and spinor particles across various geometries, revealing contrasting effects based on curvature sign and particle spin.

## Contribution

It provides new calculations of pair production rates on curved spaces with magnetic fields, highlighting the differential impact of curvature and magnetic backgrounds on scalars and spinors.

## Key findings

- Positive curvature enhances scalar pair production and suppresses spinor production.
- Negative curvature suppresses scalar pair production and enhances spinor production.
- Magnetic fields further modify these effects depending on the curvature and particle spin.

## 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.