  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.
