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

Understand

We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) D containing the pseudodifferential operator $\Box^{1-\alpha}$, 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.