A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions

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 ${\epsilon }_{\alpha \beta \gamma }$. 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.

LaTeX, 17 pages, expanded reference list and discussion of relationship to previous work

References in corpus (2)

• Chern-Simons Theory as the Large Mass Limit of Topologically Massive Yang-Mills Theory
• On the infrared limit of the Chern-Simons-Proca theory

Cited by in corpus (6)

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• Two-Loop Quantum Corrections of Scalar QED with Non-Minimal Chern-Simons Coupling
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• Relating Quantum Information to Charged Black Holes
• Non-abelian self-duality from self-interaction