  We consider the Dirac equation in flat Minkowski 3-space and rewrite it as
the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is
defined as the dual of the electromagnetic vector potential. Our model clearly
distinguishes the electron and the positron without resorting to "negative
frequencies": we produce a real scalar invariant (charge) which indicates
whether we are looking at an electron or a positron. Another interesting
feature of our model is that the free electron and positron are identified with
gradient type solutions of the standard (torsion free) Maxwell equation; such
solutions have traditionally been disregarded on the grounds of gauge
invariance.
