Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity

Bais, F.A.; Muller, N. M.; Schroers, Bernd J.

doi:10.1016/s0550-3213(02)00572-2

Cited by 77 publications

(137 citation statements)

References 38 publications

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“…In fact, most systems which can be described by means of two-dimensional conformal field theory have this property (for reviews, see for instance [19,20,21]). Examples in (2+1) dimensions are the discrete gauge theories we will treat in this paper, but also (2+1)-dimensional gravity [22,23] and certain fractional quantum Hall systems [24,25]. In two spatial dimensions, the exchanges of a system of n particles are governed by the braid group B n .…”

Section: Definitionmentioning

confidence: 99%

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Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory

Bais¹,

Schroers²,

Slingerland³

2003

J. High Energy Phys.

112

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Gauge theories in 2+1 dimensions whose gauge symmetry is spontaneously broken to a finite group enjoy a quantum group symmetry which includes the residual gauge symmetry. This symmetry provides a framework in which fundamental excitations (electric charges) and topological excitations (magnetic fluxes) can be treated on equal footing. In order to study symmetry breaking by both electric and magnetic condensates we develop a theory of symmetry breaking which is applicable to models whose symmetry is described by a quantum group (quasitriangular Hopf algebra). Using this general framework we investigate the symmetry breaking and confinement phenomena which occur in (2+1)-dimensional gauge theories. Confinement of particles is linked to the formation of string-like defects. Symmetry breaking by an electric condensate leads to magnetic confinement and vice-versa. We illustrate the general formalism with examples where the symmetry is broken by electric, magnetic and dyonic condensates.The irreps of our transformation group algebras are then described by the following theorem, which is a simple consequence of theorem 3.9 in [29]

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Section: Definitionmentioning

confidence: 99%

“…the quantum group theoretical framework of [22,23]. A generalization to weak quasi-Hopf algebras would bring any physical system which has a description in terms of Chern-Simons theory or rational conformal field theory within the reach of our methods.…”

Section: Jhep05(2003)068mentioning

confidence: 99%

Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory

Bais¹,

Schroers²,

Slingerland³

2003

J. High Energy Phys.

112

View full text Add to dashboard Cite

show abstract

“…This aspect represents a crucial departure from the four dimensional case and it allows for a different approach to the quantization of the system. In order to clarify this point, let us first recall some basic elements of the inclusion of particles in 3D gravity (see, for instance, [14,[30][31][32][33][34][35] and references therein).…”

Section: Coupling To Massive Point Particlesmentioning

confidence: 99%

Symmetries of quantum spacetime in three dimensions

et al. 2016

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By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant Λ, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of so q (4), with q = exp (i ̵ h √ Λ 2κ). By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping κ finite, we obtain the kappa-Poincaré algebra of the flat quantum space-time symmetries.

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“…In this framework, the search for generalized (quantum) symmetries that leave the physical action invariant leads to deformation of the Poincaré symmetry, with κ-Poincaré symmetry being one of the ones most extensively studied [5][6][7][8][9][10][13][14][15][16][17][18][19][20][21][22] One example of a deformed relativistic symmetry that could describe the physics at the Planck scale is the κ-deformed Poincaré Hopf algebra symmetry, where κ is the deformation parameter, usually corresponding to the Planck scale. It has been shown that a quantum field theory with κ-Poincaré symmetry emerges in a certain limit of quantum gravity coupled to matter fields [23][24][25][26][27], which amounts to a non-commutative field theory on the κ-deformed Minkowski space.…”

Section: Introductionmentioning

confidence: 99%

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

Meljanac

Pikutić

2017

Eur. Phys. J. C

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Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and noncommutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

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Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity

Cited by 77 publications

References 38 publications

Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory

Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory

Symmetries of quantum spacetime in three dimensions

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

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