Gauge theories can be described by assigning a vector space ¯V (x) to each space time point x. A common set
of complex numbers, ¯ C, is usually assumed to be the set of scalars for all the ¯ Vx. This is expanded here to
assign a separate set of scalars, ¯ Cx, to ¯ Vx. The freedom of choice of bases, expressed by the action of a gauge
group operator on the ¯Vx, is expanded here to include the freedom of choice of scale factors, cy, x, as elements of GL(1, C) that relate ¯ Cy to ¯ Cx. A gauge field representation of cy,x gives two gauge fields, A(x) and iB (x).
Inclusion of these fields in the covariant derivatives of Lagrangians results in A(x) appearing as a gauge boson
for which mass is optional and B(x) as a massless gauge boson. B(x) appears to be the photon field. The nature
of A(x) is not known at present. One does know that the coupling constant of A(x) to matter fields is very small
compared to the fine structure constant.