  It has been known for a long time that the presence of torsion is in conflict
with gauge invariance of the the electromagnetic field in curved Riemann-Cartan
space if the Maxwell field is minimally coupled to the curved gravitational
space through the covariant derivative. In search for a possible solution, we
consider in this note the system of Maxwell-Dirac electrodynamics in
Riemann-Cartan space. Through investigating consistency of the field equations,
and taking cue from the scale invariance properties of the system, we come up
with a solution that satisfies gauge invariance without having to dispense with
torsion in the coupled Maxwell-Dirac system. This is achieved by modifying the
connection that appears in the covariant derivative for the Maxwell field. The
modified connection turns out to be in the form of a Weyl connection, with the
torsion trace vector playing the effective role of a Weyl gauge field. With
this modified connection, which is symmetrical, the Lorentz-spin current of the
photon field is seen to vanish. In addition, except for the Dirac mass term,
the system exhibits local scale invariance. The same consideration applies to
all gauge theories, abelian or non-ableian, in the standard model of particle
physics.
