  In this paper we discuss the global symmetries and the renormalizibility of
Lee-Wick 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
two-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.
