摘要：This work presents a method of grouping the electron spinors and the phonon modes of metal oxide crystals such as vanadium dioxide 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 $${ ext{M}}_{)}$$- and $${ ext{M}}_{,}$$-$${ ext{VO}}_{,}$$, while the longitudinal mode is neutral. A generalization of 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 results in violation of this discrete Ward-Takahashi identity for interband transitions, resulting in scattering from the longitudinal component. Thus both the spinors and the bosons acquire mass and an electronic band gap and optical phonon modes result: a symmetry-breaking metal-insulator transition, which can manifest concurrent spin-ordering.
