Abstract
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.
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