  We analyze the stress-energy tensor for the self-coupled Maxwell-Dirac system
in the bilinear current formalism, using two independent approaches. The first
method used is that attributed to Belinfante: starting from the spinor form of
the action, the well-known canonical stress-energy tensor is augmented, by
extending the Noether symmetry current to include contributions from the
Lorentz group, to a manifestly symmetric form. This form admits a transcription
to bilinear current form. The second method used is the variational derivation
based on the covariant coupling to general relativity. The starting point here
at the outset is the transcription of the action using, as independent field
variables, both the bilinear currents, together with a gauge invariant vector
field (a proxy for the electromagnetic vector potential). A central feature of
the two constructions is that they both involve the mapping of the Dirac
contribution to the stress-energy from the spinor fields to the equivalent set
of bilinear tensor currents, through the use of appropriate Fierz identities.
Although this mapping is done at quite different stages, nonetheless we find
that the two forms of the bilinear stress-energy tensor agree. Finally, as an
application, we consider the reduction of the obtained stress-energy tensor in
bilinear form, under the assumption of spherical symmetry.
