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arXiv · 1408.1637

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

E. C. Marino·Leandro O. Nascimento·Van Sérgio Alves·C. Morais Smith
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Abstract

We examine the unitarity of a class of generalized Maxwell U(1) gauge theories in (2+1) D containing the pseudodifferential operator $\Box^{1-α}$, for $α\in [0,1)$. We show that only Quantum Electrodynamics (QED$_3$) and its generalization known as Pseudo Quantum Electrodynamics (PQED), 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 hetero-junctions displaying the quantum Hall effect.

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E. C. Marino, Leandro O. Nascimento, Van Sérgio Alves, C. Morais Smith. 2014-08-07. Unitarity of theories containing fractional powers of the d'Alembertian operator. https://doi.org/10.1103/physrevd.90.105003

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