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) D containing the pseudodifferential operator ${\square }^{1-\alpha }$, for $\alpha \in [0,1)$. We show that only Quantum Electrodynamics (QED${}_3$) and its generalization known as Pseudo Quantum Electrodynamics (PQED), for which $\alpha =0$ and $\alpha =1/2$, 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 hetero-junctions displaying the quantum Hall effect.

6 pages, no figures

References in corpus (2)

• The electronic properties of graphene
• Electromagnetic current correlations in reduced quantum electrodynamics

Cited by in corpus (4)

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• Bosonization, mass generation, and the pseudo Chern-Simons action
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation