New realizations of Lie algebra kappa-deformed Euclidean space

Meljanac, Stjepan; Stojić, Marko

doi:10.1140/epjc/s2006-02584-8

Cited by 145 publications

(349 citation statements)

References 34 publications

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“…Furthermore it has been shown that the space-times associated with a variety of black holes at the Planck scale could be described by a κ-Minkowski algebra [16][17][18]. In this paper we shall take the κ-Minkowski algebra [19][20][21][22][23][24][25][26][27][28] as the prototype of a space-time at the Planck scale and shall investigate various features of QNM's and associated physics in that background.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

Gupta¹,

Jurić²,

Samsarov³

2017

J. High Energ. Phys.

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Abstract:We analyze the fermionic quasinormal modes of the BTZ black hole in the presence of space-time noncommutativity. Our analysis exploits a duality between a spinless and spinning BTZ black hole, the spin being proportional to the noncommutative deformation parameter. Using the AdS/CFT correspondence we show that the horizon temperatures in the dual CFT are modified due to noncommutative contributions. We demonstrate the equivalence between the quasinormal and non-quasinormal modes for the noncommutative fermionic probes, which provides further evidence of holography in the noncommutative setting. Finally we present an analysis of the emission of Dirac fermions and the corresponding tunneling amplitude within this noncommutative framework.

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Section: Introductionmentioning

confidence: 99%

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

Gupta¹,

Jurić²,

Samsarov³

2017

J. High Energ. Phys.

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“…This paper is a continuation of earlier work [6,7], following [8], whose aim is systematically to construct κ-deformed quantum field theory from the following particular perspective. (Other approaches can be found in [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].) We recall the viewpoint on quantum field theory taken by Weinberg in [25], namely that quantum field theory takes the form it does because this is essentially the only way to construct a quantum mechanical theory of point particles with Poincaré symmetry -given only a very limited number of additional physical principles, like cluster decomposition.…”

Section: Introductionmentioning

confidence: 99%

On κ-deformation and triangular quasibialgebra structure

Young

Zegers

2009

Nuclear Physics B

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We show that, up to terms of order κ −5 , the κ-deformed Poincaré algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the context of κ-deformed quantum field theory, we argue that this structure, assuming it exists to all orders, ensures that states of any number of identical particles, in any representation, can be defined in a κ-covariant fashion.

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“…An example of this more general class is provided by the κ-deformed space [3,4,5], which is based on a Lie algebra type noncommutativity. Apart from its algebraic aspects [6,7,8,9,10,11], various features of field theories and symmetries on κ-deformed spaces have recently been studied [12,13,14,15,16]. Such a space has also been discussed in the context of doubly special relativity [17,18,19].…”

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confidence: 99%

Twisted statistics inκ-Minkowski spacetime

et al. 2008

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We consider the issue of statistics for identical particles or fields in κ-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription. I. INTRODUCTIONNoncommutative geometry is a plausible candidate for describing physics at the Planck scale, a simple model of which is given by the Moyal plane [1]. The models of noncommutative spacetime that follow from combining general relativity and uncertainty principle can be much more general [2]. An example of this more general class is provided by the κ-deformed space [3,4,5], which is based on a Lie algebra type noncommutativity. Apart from its algebraic aspects [6,7,8,9,10,11], various features of field theories and symmetries on κ-deformed spaces have recently been studied [12,13,14,15,16]. Such a space has also been discussed in the context of doubly special relativity [17,18,19].The issue of particle statistics plays a central role in the quantum description of a many-body system or field theory. This issue has naturally arisen in the context of noncommutative quantum mechanics and field theory [20,21,22,23,24]. In the noncommutative case, the issue of statistics is closely related to the symmetry of the noncommutative spacetime on which the dynamics is being studied. If a symmetry acts on a noncommutative spacetime, its coproduct usually has to be twisted in order to make the symmetry action compatible with the algebraic structure. In the commutative case, particle statistics is superselected, i.e. it is preserved under the action of the symmetry. In the presence of noncommutativity, it is thus natural to demand that the statistics is invariant under the action of the twisted symmetry. This condition leads to a new twisted flip operator, which is compatible with the twisted coproduct of the symmetry group [22,23]. The operators projecting to the symmetric and antisymmetric sectors of the Hilbert space are then constructed from the twisted flip operator. While most of the discussion of statistics in the noncommutative setup has been done in the context of the Moyal plane, some related ideas for κ-deformed spaces have also appeared recently [25,26,27].In this paper we set up a general formalism to describe statistics in κ-deformed spaces. Our formalism presented here is applicable to a system with an arbitrary symmetry group, which may include Poincare, Lorentz, Euclidean * trg@imsc.res.in † kumars.gupta@saha.ac.in ‡ harisp@uohyd.ernet.in § meljanac@irb.hr ¶ dmeljan@irb.hr

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New realizations of Lie algebra kappa-deformed Euclidean space

Cited by 145 publications

References 34 publications

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

On κ-deformation and triangular quasibialgebra structure

Twisted statistics inκ-Minkowski spacetime

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