  This work presents a method of grouping the electron spinors and the acoustic
phonon modes of polar crystals such as metal oxides into an SU(2) gauge theory.
The gauge charge is the electron spin, which is assumed to couple to the
transverse acoustic phonons on the basis of spin ordering phenomena in crystals
such as V$_{2}$O$_{3}$ and VO$_{2}$, while the longitudinal mode is neutral. A
generalization the Peierls mechanism is presented based on the discrete gauge
invariance of crystals and the corresponding Ward-Takahashi identity. The
introduction of a band index violates the Ward-Takahashi identity for interband
transitions resulting in a longitudinal component appearing in the upper phonon
band. Thus both the spinors and the vector bosons acquire mass and a crystal
with an electronic band gap and optical phonon modes results. In the limit that
the coupling of bosons charged under the SU(2) gauge group goes to zero,
breaking the electron U(1) symmetry recovers the BCS mechanism. In the limit
that the neutral boson decouples, a Cooper instability mediated by spin-wave
exchange results from symmetry breaking, i.e. unconventional superconductivity
mediated by magnetic interactions.
