Electrodynamics of Charged Vector Bosons

Abstract

The interaction of a quantized charged vector boson in the presence of an external electromagnetic field is considered. A nonsingular electromagnetic current operator is obtained by separating the points of the field operators by a small spacelike distance ${\ensuremath{\epsilon}}^{\ensuremath{\mu}}$ in a gauge-invariant fashion (analogous to the construction of the current operator of spinor electrodynamics). It is shown that the matrix element of the current is gauge-invariant, divergenceless in the limit ${\ensuremath{\epsilon}}^{\ensuremath{\mu}}\ensuremath{\rightarrow}0$, and no more than logarithmically singular, to all orders of the external electromagnetic field. The resultant theory is seen consequently to be gauge-invariant and to be renormalizable.