We calculate the pair production rates for spin-1 or vector particles on
spaces of the form M×R1,1 with M corresponding to
R2 (flat), S2 (positive curvature) and H2 (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 S2 and H2 is obtained. We also
give a brief discussion of how our results relate to ideas about confinement in
nonabelian theories.Comment: 24 pages, 9 figure