Dispersion relations in noncommutative theories

Abstract

We present a detailed study of plane waves in noncommutative abelian gauge theories. The dispersion relation is deformed from its usual form whenever a constant background electromagnetic field is present and is similar to that of an anisotropic medium with no Faraday rotation nor birefringence. When the noncommutativity is induced by the Moyal product we find that for some values of the background magnetic field no plane waves are allowed when time is noncommutative. In the Seiberg-Witten context no restriction is found. We also derive the energy-momentum tensor in the Seiberg-Witten case. We show that the generalized Poynting vector obtained from the energy-momentum tensor, the group velocity and the wave vector all point in different directions. In the absence of a constant electromagnetic background we find that the superposition of plane waves is allowed in the Moyal case if the momenta are parallel or satisfy a sort of quantization condition. We also discuss the relation between the solutions found in the Seiberg-Witten and Moyal cases showing that they are not equivalent.

Born–infeld Electrodynamics and Euler–heisenberg-Like Model: Outstanding Examples of the Lack of Commutativity Among Quantized Truncated Actions and Truncated Quantized Actions

“…Also, the study of space-time noncommutativity on light propagation in a background electromagnetic field has been discussed along these lines. [15][16][17] In this perspective, it should be mentioned that recently considerable attention has been paid to the study of nonlinear electrodynamics (Born-Infeld theory) due to its natural emergence from D-brane physics. 18,19 In addition to the string interest, Born-Infeld theory has also been investigated from quite different viewpoints.…”

Properties of noncommutative axionic electrodynamics

“…Another possible scenario is the existence of millicharged particles [14]. In addition, the study of spacetime noncommutativity on light propagation in a background electromagnetic field has also attracted interest in order to account the results reported by the PVLAS collaboration [15][16][17]. In particular, the noncommutative axionic electrodynamics version has been considered [16] within the framework of the Lorentz-violating extension of QED [18].…”

The Photon Dispersion as an Indicator for New Physics?

“…Hence people quickly proceeded to a supersymmetric version of this model, where the negative IR divergence is cancelled [14]. (It is not visible either, of course, when one treats the model classically [15].) However, we were not happy with this combination of daring hypotheses, so we did not assume supersymmetry in addition.…”