Redefining Spinors in Lorentz-Violating QED

Abstract

An analysis of spinor redefinitions in the context of the Lorentz-violating QED extension is performed. Certain parameters that apparently violate Lorentz invariance are found to be physically irrelevant as they can be removed from the lagrangian using an appropriate redefinition of the spinor field components. It is shown that conserved currents may be defined using a modified action of the complex extension of the Lorentz group on the redefined spinors. This implies a natural correspondence between the apparently Lorentz-violating theory and conventional QED. Redefinitions involving derivatives are shown to relate certain terms in the QED extension to lagrangians involving nonlocal interactions or skewed coordinate systems. The redundant parameters in the QED extension are identified and the lagrangian is rewritten in terms of physically relevant coupling constants. The resulting lagrangian contains only physically relevant parameters and transforms conventionally under Lorentz transformations.