Abstract
In the current paper, 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.
Highlights
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. It supports a better understanding of the electromagnetic sector of the nonminimal standard model extension (SME)
Violations of Lorentz invariance have been hypothesized to emerge from phenomena related to Planck-scale physics such as strings [1], spin networks described by loop quantum gravity [2], noncommutative spacetimes [3], spacetime foam [4], nontrivial spacetime topologies [5], and effects connected to UV completions of general relativity with Horava-Lifshitz gravity [6] as a prominent example
We propose a framework of an electromagnetism modified by nonminimal Lorentz violation in (1 þ 2) spacetime dimensions
Summary
Violations of Lorentz invariance have been hypothesized to emerge from phenomena related to Planck-scale physics such as strings [1], spin networks described by loop quantum gravity [2], noncommutative spacetimes [3], spacetime foam [4], nontrivial spacetime topologies [5], and effects connected to UV completions of general relativity with Horava-Lifshitz gravity [6] as a prominent example. One possibility of obtaining planar theories from parent models defined in (1 þ 3) spacetime dimensions is by means of the procedure known as dimensional reduction This method has been used before to derive the planar version of the Maxwell-Carroll-Field-Jackiw Lagrangian [25]. Our goal is to provide a nonminimal daughter electrodynamics in (1 þ 2) dimensions The purpose of such a procedure is twofold: First, a planar Lorentz-violating electrodynamics can be valuable to describe condensedmatter phenomena that occur in two-dimensional systems. II, we apply dimensional reduction to the electromagnetic sector of the nonminimal SME Lorentz indices are denoted by Greek letters, whereas we indicate spatial indices by Latin letters
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