  In this paper we give a variation of the gauge procedure which employs a
scalar gauge field, $B (x)$, in addition to the usual vector gauge field,
$A_\mu (x)$. We study this variant of the usual gauge procedure in the context
of a complex scalar, matter field $\phi (x)$ with a U(1) symmetry. We will
focus most on the case when $\phi$ develops a vacuum expectation value via
spontaneous symmetry breaking. We find that under these conditions the scalar
gauge field mixes with the Goldstone boson that arises from the breaking of a
global symmetry. Some other interesting features of this scalar gauge model
are: (i) The new gauge procedure gives rise to terms which violate C and CP
symmetries. This may have have applications in cosmology or for CP violation in
particle physics; (ii) the existence of mass terms in the Lagrangian which
respect the new extended gauge symmetry. Thus one can have gauge field mass
terms even in the absence of the usual Higgs mechanism; (iii) the emergence of
a sine-Gordon potential for the scalar gauge field; (iv) a natural, axion-like
suppression of the interaction strength of the scalar gauge boson.
