Vector boson in constant electromagnetic field

TL;DR

This paper derives the propagator and solutions for a vector W-boson in a constant electromagnetic field, revealing how polarization and field components influence the Bogoliubov coefficients and the imaginary part of the Lagrangian.

Contribution

It provides explicit calculations of wave solutions, Bogoliubov coefficients, and the Lagrangian contributions for a vector boson with g=2 in constant electromagnetic fields, extending scalar and Dirac particle results.

Findings

Bogoliubov coefficients are polarization-independent in pure electric fields.

Coefficients for perpendicular spin states match scalar boson case.

Interactions depend on magnetic field through shifted mass terms.

Abstract

The propagator and complete sets of in- and out-solutions of wave equation, together with Bogoliubov coefficients, relating these solutions, are obtained for vector $W$-boson (with gyromagnetic ratio $g=2$) in a constant electromagnetic field. When only electric field is present the Bogoliubov coefficients are independent of boson polarization and are the same as for scalar boson. When both electric and magnetic fields are present and collinear, the Bogoliubov coefficients for states with boson spin perpendicular to the field are again the same as in scalar case. For $W^-$ spin along (against) the magnetic field the Bogoliubov coefficients and the contributions to the imaginary part of the Lagrange function in one loop approximation are obtained from corresponding expressions for scalar case by substitution $m^2\to m^2+2eH$ $(m^2\to m^2-2eH)$. For gyromagnetic ratio $g=2$ the vector boson interaction with constant electromagnetic field is described by the functions, which can be expected by comparing wave functions for scalar and Dirac particle in constant electromagnetic field.