Abstract

The Lagrangian density $$\frac{1}{2}i\bar \psi (x)[\gamma ^\mu (x)\vec D_\mu - \vec D_\mu \gamma ^\mu (x)] - m\bar \psi (x)\psi (x) + \frac{1}{{128a^2 }}tr[\overline {D_\mu \gamma ^\mu (x)} D_\nu \gamma ^\nu (x)]$$ is shown to be invariant under localU(2, 2) spin-gauge transformations where γ u (x)D μ is a localU(2, 2) covariant derivative, $$\{ \psi (x),\bar \psi (x)\} $$ are Dirac bispinor fields and γμ(x) is a vector field with values in a Dirac algebra. It is also shown that spin-gauge fixings exist such that the bispinor field couplings can all be expressed as electromagnetic couplings which include only scalar and axial vector couplings in addition to the standard and Pauli couplings. By the localU(2, 2) symmetry-breaking constraints ∂νγμ(x)=0 and further gauge fixings, it is shown that the Lagrangian density term $$tr\overline {[D_\mu \gamma ^\mu (x)} D_\nu \gamma ^\nu (x)]$$ includes only a mass term for an axial vector field in addition to all the terms in the standard Lagrangian density which describe the electromagnetic field and control infrared and ultraviolet divergences.

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