Pair production of massive charged vector bosons from the worldline

TL;DR

This paper develops a worldline approach to describe massive charged vector bosons interacting with electromagnetic fields, deriving pair production rates and vacuum instability results consistent with quantum field theory.

Contribution

It introduces a novel worldline formulation for massive spin-1 particles, demonstrating its consistency and reproducing known quantum field theory results for pair production.

Findings

Derived the one-loop effective Lagrangian for charged vector bosons in a constant electromagnetic field.

Quantified vacuum instability and pair production rate for massive charged vector bosons.

Validated the worldline approach by matching results with standard quantum field theory calculations.

Abstract

We investigate a worldline formulation for a massive spin-1 particle interacting with an electromagnetic background. Two first-quantized descriptions of the spin degrees of freedom are considered: one based on bosonic oscillators and the other on fermionic oscillators. Focusing initially on the bosonic model -- which can accommodate particles of arbitrary integer spin -- we review how quantization in the spin-1 sector, performed both via Dirac's method and BRST quantization, reproduces the free Proca field theory. We then introduce coupling to an external electromagnetic field and demonstrate that Maxwell's equations for the background emerge as a consistency condition for the nilpotency of the BRST charge on the spin-1 sector. Encouraged by this result, which proves the viability of the particle model, we proceed to construct 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 massive charged vector boson. As expected, the result reveals a vacuum instability, which we quantify by deriving the pair production rate for the vector bosons, recovering previous results obtained in quantum field theory. For comparison, we repeat the analysis using the standard $\mathcal{N}=2$ spinning particle model, which contains fermionic worldline degrees of freedom, finding identical results. Finally, we comment on possible extensions of the worldline models to include effective interactions and briefly explore their implications for pair production.