  In this work we employ a field theoretical approach to explain the nature of
the non-conserved spin current in spintronics. In particular, we consider the
usual U(1) gauge theory for the electromagnetism at classical level in order to
obtain the broken continuity equation involving the spin current and
spin-transfer torque. Inspired in the recent work of A. Vernes, B. L. Gyorffy
and P. Weinberger where they obtain such equation in terms of relativistic
quantum mechanics, we formalize their result in terms of the well known
currents of field theory such as the Bargmann-Wigner current and the chiral
current. Thus, an interpretation of spintronics is provided in terms of Noether
currents (conserved or not) and symmetries of the electromagnetism. In fact,
the main result of the present work is that the non-conservation of the spin
current is associated to the gauge invariance of physical observables where the
breaking term is proportional to the chiral current. Moreover, we generalize
their result by including the electromagnetic field as a dynamical field
instead of an external one.
