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A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions

F. A. Dilkes·D. G. C. McKeon
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Abstract

The standard formulation of a massive Abelian vector field in $2+1$ dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term. In this latter model, we still have a massive vector field, but now the interaction with a charged spinor field is renormalizable (as opposed to super renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg auxiliary scalar field decouples from the vector field. The one-loop spinor self energy is computed using operator regularization, a technique which respects the three dimensional character of the antisymmetric tensor $ε_{αβγ}$. This method is used to evaluate the vector self energy to two-loop order; it is found to vanish showing that the beta function is zero to two-loop order. The canonical structure of the model is examined using the Dirac constraint formalism.

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F. A. Dilkes, D. G. C. McKeon. 1995-06-09. A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions. https://doi.org/10.1103/physrevd.52.4668

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