Light propagation in a background field for time–space non-commutativity and axionic non-commutative QED

Chatillon, N.; Pinzul, A.

doi:10.1016/j.nuclphysb.2006.12.003

Cited by 18 publications

(31 citation statements)

References 58 publications

(76 reference statements)

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“…This reproduces the results found in [10,11,12,19] for several particular cases. Notice that the frequency is now dependent on the direction of wave vector, a characteristic of anisotropic media.…”

Section: Seiberg-witten Map Picturesupporting

confidence: 90%

Dispersion relations in noncommutative theories

2007

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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.

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Section: Seiberg-witten Map Picturesupporting

confidence: 90%

Dispersion relations in noncommutative theories

2007

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“…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].…”

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confidence: 99%

“…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].On the other hand, axionic electrodynamics experiences mass generation due to the breaking of rotational invariance induced by a classical background configuration of the gauge field strength [19], and leads to confining potentials in the presence of nontrivial constant expectation values for the gauge field strength F [20]. In fact, in the case of a constant electric field strength expectation value the static potential remains Coulombic, while in the case of a constant magnetic field strength expectation value the potential energy is the sum of a Yukawa and a linear potential, leading to the confinement of static charges.…”

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confidence: 99%

Properties of noncommutative axionic electrodynamics

Gaete

Schmidt

2007

Phys. Rev. D

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Using the gauge-invariant but path-dependent variables formalism, we compute the static quantum potential for noncommutative axionic electrodynamics, and find a radically different result than the corresponding commutative case. We explicitly show that the static potential profile is analogous to that encountered in both non-Abelian axionic electrodynamics and in Yang-Mills theory with spontaneous symmetry breaking of scale symmetry.Comment: 4 pages. To appear in PR

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“…Up to the first order in θ µν , NC quantum field theory with constant noncommutativity is just a special case of the general situation (e.g., see discussion in [5]). The quantization of NC field theories (NCFT) had been performed within this framework, i.e quantization of a Lorentz violating theory.…”

Section: Introductionmentioning

confidence: 99%

UV/IR mixing as a twisted Poincaré anomaly

Pinzul¹

2012

J. Phys. A: Math. Theor.

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We analyze symmetries of the 1-loop effective action of φ 4 noncommutative field theory. It is shown, that despite the twisted Poincaré invariance of the classical noncommutative action, its 1-loop quantum counterpart lacks this invariance. Though Noether analysis of the model is somewhat obscure, it is still possible to interpret this symmetry breaking as a quantum anomaly due to inappropriate choice of the quantization method. * apinzul@unb.br 1 IntroductionBased on a quite general argument [1], it is believed that one or another form of a noncommutative (NC) space-time should emerge as a quasi-classical approximation to quantum gravity in a sense that quantum fields on such a space-time will probe the quantum gravity scale through noncommutativity. This observation, as well as the appearance of NC field theory in super strings [2], sparked considerable interest in noncommutative physics. Most of the efforts have been devoted to the analysis of theories on a NC space-time with constant noncommutativity, a so-called Moyal space. (Literature on the subject is vast, for a review see, e.g. [3]) This is the simplest possible type of noncommutativity, defined by the following commutation relation between the coordinatesHere θ µν gives the scale of quantum gravity, usually it is thought to be related to the Planck scale. It is clear that if θ µν is some non-dynamical constant, which is the case in string theory, then (1) breaks Lorentz invariance.The study of Lorentz-breaking theories has a long history by now [4]. Up to the first order in θ µν , NC quantum field theory with constant noncommutativity is just a special case of the general situation (e.g., see discussion in [5]). The quantization of NC field theories (NCFT) had been performed within this framework, i.e quantization of a Lorentz violating theory. Perturbative analysis led to some noncommutative corrections but also, what is more important, to a quite universal property of NCFT -UV/IR mixing [6]. (Though, see some recent proposals on models without UV/IR mixing [7][8][9].) This property, which is due to the non-local nature of noncommutativity, put an end to hopes that noncommutativity (at least in the simple form of a constant θ µν ) would serve as a UV regulator, which was the major motivation for one of the first works on a NC space-time [10].After works [11,12], another possibility to look at NCFT had become possible: instead of thinking in terms of broken Lorentz invariance, one could now think about NCFT as a theory with preserved, but twisted Lorentz symmetry.1 On the classical level, this is just a point of view that does not add anything new to the picture. But the transition to quantization changes the situation drastically: one has to maintain this new twisted symmetry on quantum level. Essentially, there exist two approaches to quantization of NCFT with twisted Lorentz symmetry:• The quantization should be done according to the usual rules. In other words, the usual Feynman rules, derived from the path integral with the standard quant...

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Light propagation in a background field for time–space non-commutativity and axionic non-commutative QED

Cited by 18 publications

References 58 publications

Dispersion relations in noncommutative theories

Dispersion relations in noncommutative theories

Properties of noncommutative axionic electrodynamics

UV/IR mixing as a twisted Poincaré anomaly

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