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Title: 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.

Authors:
; ;  [1];  [2]
  1. Departamento de Fisica, Universidade Federal da Paraiba, 58051-970, Joao Pessoa, PB (Brazil)
  2. (Brazil)
Publication Date:
OSTI Identifier:
21010933
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.025020; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; COMMUTATION RELATIONS; DISPERSION RELATIONS; ELECTROMAGNETIC FIELDS; ENERGY-MOMENTUM TENSOR; FARADAY EFFECT; GAUGE INVARIANCE; MAGNETIC FIELDS; MATHEMATICAL SOLUTIONS; POYNTING THEOREM; QUANTIZATION; QUANTUM FIELD THEORY; VECTORS; WAVE PROPAGATION

Citation Formats

Mariz, Tiago, Nascimento, J. R., Rivelles, Victor O., and Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP. Dispersion relations in noncommutative theories. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.025020.
Mariz, Tiago, Nascimento, J. R., Rivelles, Victor O., & Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP. Dispersion relations in noncommutative theories. United States. doi:10.1103/PHYSREVD.75.025020.
Mariz, Tiago, Nascimento, J. R., Rivelles, Victor O., and Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP. Mon . "Dispersion relations in noncommutative theories". United States. doi:10.1103/PHYSREVD.75.025020.
@article{osti_21010933,
title = {Dispersion relations in noncommutative theories},
author = {Mariz, Tiago and Nascimento, J. R. and Rivelles, Victor O. and Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.025020},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}