Dimensional reduction of the electromagnetic sector of the nonminimal standard model extension

We construct a Lorentz-violating electrodynamics in ( 1 + 2 ) spacetime dimensions from the electromagnetic sector of the nonminimal standard model extension (SME) in ( 1 + 3 ) dimensions. Subsequently, we study some of the basic properties of this framework. We obtain the field equations, the Green...

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Bibliographic Details
Published in:Physical review. D 2019-11, Vol.100 (9), p.1, Article 095026
Main Authors: Reis, João A. A. S., Ferreira, Manoel M., Schreck, Marco
Format: Article
Language:English
Subjects:
Condensed matter physics
Electrodynamics
Gauge invariance
Green's functions
Mathematical models
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Summary:We construct a Lorentz-violating electrodynamics in ( 1 + 2 ) spacetime dimensions from the electromagnetic sector of the nonminimal standard model extension (SME) in ( 1 + 3 ) dimensions. Subsequently, we study some of the basic properties of this framework. We obtain the field equations, the Green's functions, and the perturbative Feynman rules. Furthermore, the modified dispersion relations are computed at leading order in Lorentz violation. We then remove the unphysical degrees of freedom from the electromagnetic Green's function that are present due to gauge invariance. The resulting object is used to construct the general solutions of the uncoupled field equations with external inhomogeneities present. This modified planar electrodynamics may be valuable to describe electromagnetic phenomena in two-dimensional condensed-matter systems. Furthermore, it supports a better understanding of the electromagnetic sector of the nonminimal SME.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.100.095026