Charged massive vector bosons from the worldline

A worldline formulation for charged, massive spin-1 particle is presented through two distinct models. First, a model with bosonic oscillators on the worldline is considered. We extend it to describe massive integer spin particles and, via both Dirac and BRST quantization, the free Proca field theory is reproduced in the spin-1 sector. The coupling of the model to an external electromagnetic field is consistent only for on-shell backgrounds, as determined by the nilpotency of the BRST charge. For such configurations, we perform a path integral quantization of the worldline action for the charged spin-1 particle on the circle. This yields the one-loop effective Lagrangian for a constant electromagnetic field induced by a charged massive vector boson. From the Lagrangian, we quantify vacuum instability by computing the pair production rate for massive vector bosons. Our results confirm previous findings obtained in quantum field theory. Finally, for comparison, we repeat the analysis using the standard N = 2 spinning particle model, which contains fermionic worldline degrees of freedom, and obtain identical results.