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Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED

B. Altschul
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Abstract

We consider a Lorentz-violating modification to the fermionic Lagrangian of QED that is known to produce a finite Chern-Simons term at leading order. We compute the second order correction to the one-loop photon self-energy in the massless case using an exact propagator and a nonperturbative formulation of the theory. This nonperturbative theory assigns a definite value to the coefficient of the induced Chern-Simons term; however, we find that the theory fails to preserve gauge invariance at higher orders. We conclude that the specific nonperturbative value of the Chern-Simons coefficient has no special significance.

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B. Altschul. 2004-02-11. Failure of Gauge Invariance in the Nonperturbative Formulation of Massless Lorentz-Violating QED. https://doi.org/10.1103/physrevd.69.125009

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