Dispersion relations in noncommutative theories

Journal Article · Mon Jan 15 04:00:00 EST 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.025020· OSTI ID:21010933

Mariz, Tiago; Nascimento, J R; Rivelles, Victor O ^[1]

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1. Departamento de Fisica, Universidade Federal da Paraiba, 58051-970, Joao Pessoa, PB (Brazil)

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.

• OSTI ID: 21010933
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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