Magnetic field and curvature effects on pair production. II. Vectors and implications for chromodynamics

We calculate the pair production rates for spin-1 or vector particles on spaces of the form $M×{R}^{1,1}$, with $M$ corresponding to ${R}^{2}$ (flat), ${S}^{2}$ (positive curvature), and ${H}^{2}$ (negative curvature), with and without a background (chromo)magnetic field on $M$. Beyond highlighting the effects of curvature and background magnetic field, this is particularly interesting since vector particles are known to suffer from the Nielsen-Olesen instability, which can dramatically increase pair production rates. The form of this instability for ${S}^{2}$ and ${H}^{2}$ is obtained. We also give a brief discussion of how our results relate to ideas about confinement in non-Abelian theories.