UC San Diego

In this paper we discuss the global symmetries and the renormalizability of Lee-Wick (LW) scalar QED. In particular, in the "auxiliary-field" formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the auxiliary-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are constrained by the joint conditions of gauge and SO(1,1) invariance. We also compute the one-loop beta functions in LW scalar QED and contrast them with those of ordinary scalar QED. © 2010 The American Physical Society.