Unitarity of theories containing fractional powers of the d'Alembertian operator

Abstract

We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) dimensions containing the pseudodifferential operator □1-α, for α [0,1). We show that only QED3 and its generalization known as pseudo-QED, for which α=0 and α=1/2, respectively, satisfy unitarity. The latter plays an important role in the description of the electromagnetic interactions of charged particles confined to a plane, such as in graphene or in heterojunctions displaying the quantum Hall effect. Possible implications of our results on the role of unitarity in the framework of the AdS/CFT correspondence are briefly pointed out at the end.