SCALAR FIELD THEORY ON Κ-Minkowski SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

Meljanac, Stjepan; Samsarov, Andjelo

doi:10.1142/s0217751x11051536

Cited by 50 publications

(79 citation statements)

References 89 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They indicate the weight with which coordinate x α is attached to the first, i.e. to the second part of the tensor product in (54). It is now straightforward to show that coproducts (52) and (53) can be reproduced from primitive coproducts (27) via twist (54),…”

Section: Twisted Oscillator Algebra In the Noncommutative Black Hole mentioning

confidence: 99%

See 1 more Smart Citation

Quantum statistics and noncommutative black holes

2012

Self Cite

View full text Add to dashboard Cite

We study the behaviour of a scalar field coupled to a noncommutative black hole which is described by a κ-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation parameter vanishes. The twisted flip operator is independent of the choice of realization within this class. We demonstrate that the R-matrix is quasi-triangular up to the first order in the deformation parameter. Our results indicate how a scalar field might behave in the vicinity of a black hole at the Planck scale.Keywords: κ deformed space, noncommutative black holes, twisted statistics PACS numbers: 11.10.Nx, 11.30.Cp INTRODUCTIONNoncommutative geometry offers a framework for describing the quantum structure of space-time at the Planck scale [1]. Einstein's theory of general relativity together with the uncertainty principle of quantum mechanics leads to a class of models with space-time noncommutativity [2,3]. The smooth space-time geometry of classical general relativity is thus replaced with a Hopf algebra at the Planck scale. There are many examples of such Hopf algebras including the Moyal plane, κ-space and Snyder space. The analysis of [2, 3] does not suggest any preferred choice among these models.Further insight about the possible features of the space-time algebra at the Planck scale comes from the analysis of noncommutative black holes. The algebraic structure associated with a noncommutative black hole can be revealed by studying a simple toy model, such as the noncommutative deformation of the BTZ black hole [4,5]. The resulting space-time algebra resembles a noncommutative cylinder [6,7], belonging to the general class of κ-deformed space-time [8][9][10][11]. The appearance of the κ-cylinder algebra is not restricted to the deformation of the BTZ black hole alone. Such an algebra describes noncommutative Kerr black holes [12] within the framework of twisted gravity theories [13][14][15]. It also appears in the context of noncommutative FRW cosmologies [16]. In addition, the κ-Minkowski algebra is relevant in models of doubly-special relativity and in the analysis of astrophysical data from the GRB's [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. This wide-ranging appearance of the κ-cylinder algebra * kumars.gupta@saha.ac.in † meljanac@irb.hr ‡ asamsarov@irb.hr suggests that it captures certain generic features of noncommutative gravity and black holes and is therefore an interesting toy model to explore Planck scale physics. In this Letter we shall investigate certain features of the κ-cylinder algebra using a scalar field as a simple probe. In order to study quantum field theory in any space-time, it is essential to specify the statistics of the quantum field. It has been known for a long time that quantum gravity can admit exotic statistics [31][32][33]. More recently, the idea of twisted statistics and the associated R-matrices have appeared in the context of quantum field theories in noncommutative space-time [34][35][36][37][38][39], including the κ-d...

show abstract

Section: Twisted Oscillator Algebra In the Noncommutative Black Hole mentioning

confidence: 99%

“…The statistics flip operator in this setting can be calculated from (35) by using twist element (54), leading finally to the R-matrix in the first order in a 0 , given by…”

Section: Twisted Oscillator Algebra In the Noncommutative Black Hole mentioning

confidence: 99%

Quantum statistics and noncommutative black holes

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…Much interest has been generated in the study of the physical consequences emerging from the κ-deformation of Poincaré symmetry, e.g. construction of field theories [5], [6], [7], [8], electrodynamics [9], [10] and geodesic equation [11] on κ-Minkowski spacetime and a modification of the particle statistics [12], [13], [14]. κ-deformed Poincaré symmetry is algebraically described by the κ-Poincaré Hopf algebra and is an example of deformed relativistic symmetry that can possibly describe physical reality at the Planck scale.…”

Section: Introductionmentioning

confidence: 99%

κ-deformation of phase space; generalized Poincaré algebras and R-matrix

Meljanac

Samsarov

Štrajn

2012

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We deform a phase space ( Heisenberg algebra and corresponding coalgebra) by twist. We present undeformed and deformed tensor identities that are crucial in our construction. Coalgebras for the generalized Poincaré algebras have been constructed. The exact universal R-matrix for the deformed Heisenberg (co)algebra is found. We show, up to the third order in the deformation parameter, that in the case of κ-Poincaré Hopf algebra this R-matrix can be expressed in terms of Poincaré generators only. This implies that the states of any number of identical particles can be defined in a κ-covariant way.

show abstract

“…The Lie algebra an(n), when its generators are identified with space-time coordinates, is known in the literature as the n + 1-dimensional κ-Minkowski space. For further technical details on κ-deformations the interested reader can consult [37][38][39][40][41][42][43][44][45][46]. The main goal of this Section will be to show that starting from minimal ingredients, namely the structures constants the Lie algebra an(n),…”

Section: Deforming Momentum Space To the An (N) Groupmentioning

confidence: 99%

Deformed phase spaces with group valued momenta

Arzano

Nettel

2016

Phys. Rev. D

View full text Add to dashboard Cite

We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the n-dimensional generalization of the κ-deformed momentum space and the SL(2, Ê) momentum space in three space-time dimensions. We discuss classical momentum observables associated to multi-particle systems and argue that these combine according the usual four-vector addition despite the non-abelian group structure of momentum space.

show abstract

SCALAR FIELD THEORY ON Κ-Minkowski SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

Cited by 50 publications

References 89 publications

Quantum statistics and noncommutative black holes

Quantum statistics and noncommutative black holes

κ-deformation of phase space; generalized Poincaré algebras and R-matrix

Deformed phase spaces with group valued momenta

Contact Info

Product

Resources

About