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101
Free qdeformed relativistic wave equations by representation theory
 Eur. Phys. J. C
"... In a representation theoretic approach a free qrelativistic wave equation must be such, that the space of solutions is an irreducible representation of the qPoincaré algebra. It is shown how this requirement uniquely determines the qwave equations. As examples, the qDirac equation (including qg ..."
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Cited by 13 (1 self)
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In a representation theoretic approach a free qrelativistic wave equation must be such, that the space of solutions is an irreducible representation of the qPoincaré algebra. It is shown how this requirement uniquely determines the qwave equations. As examples, the qDirac equation (including qgamma matrices which satisfy a qClifford algebra), the qWeyl equations, and the qMaxwell equations are computed explicitly. 1
Quantumgravity phenomenology: Status and prospects
, 2002
"... Over the last few years part of the quantumgravity community has adopted a more optimistic attitude toward the possibility of finding experimental contexts providing insight on nonclassical properties of spacetime. I review those quantumgravity phenomenology proposals which were instrumental in b ..."
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Cited by 12 (0 self)
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Over the last few years part of the quantumgravity community has adopted a more optimistic attitude toward the possibility of finding experimental contexts providing insight on nonclassical properties of spacetime. I review those quantumgravity phenomenology proposals which were instrumental in bringing about this change of attitude, and I discuss the prospects for the shortterm future of quantumgravity phenomenology. 1. Quantum Gravity Phenomenology The “quantumgravity problem ” has been studied for more than 70 years assuming that no guidance could be obtained from experiments. This in turn led to the assumption that the most promising path toward the solution of the problem would be the construction and analysis of very ambitious theories, some would call them “theories of everything”, capable of solving at once all of the issues raised by the coexistence of gravitation (general relativity) and quantum mechanics. In other research areas the abundant availability of puzzling experimental data encourages theorists to propose phenomenological models which solve the puzzles but are conceptually unsatisfactory on many grounds. Often those apparently unsatisfactory
HOMYANGBAXTER EQUATION, HOMLIE ALGEBRAS, AND QUASITRIANGULAR BIALGEBRAS
, 903
"... Abstract. We study a twisted version of the YangBaxter Equation, called the HomYangBaxter Equation (HYBE), which is motivated by HomLie algebras. Three classes of solutions of the HYBE are constructed, one from HomLie algebras and the others from Drinfeld’s (dual) quasitriangular bialgebras. Ea ..."
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Cited by 9 (5 self)
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Abstract. We study a twisted version of the YangBaxter Equation, called the HomYangBaxter Equation (HYBE), which is motivated by HomLie algebras. Three classes of solutions of the HYBE are constructed, one from HomLie algebras and the others from Drinfeld’s (dual) quasitriangular bialgebras. Each solution of the HYBE can be extended to operators that satisfy the braid relations. Assuming an invertibility condition, these operators give a representation of the braid group. 1.
Nonholonomic Clifford Structures and Noncommutative Riemann–Finsler Geometry
"... We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generi ..."
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Cited by 9 (8 self)
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We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generic off–diagonal metric structure (with an additional affine connection possessing nontrivial torsion) is equivalent to a generalized Lagrange, or Finsler, geometry modeled on nonholonomic manifolds. This results in the problem of constructing noncommutative geometries with local anisotropy, in particular, related to geometrization of classical and quantum mechanical and field theories, even if we restrict our considerations only to commutative and noncommutative Riemannian spaces. We elaborate a geometric approach to the Clifford modules adapted to nonlinear connections, to the theory of spinors and the Dirac operators on nonholonomic spaces and consider possible generalizations to noncommutative geometry. We argue that any commutative Riemann–Finsler geometry and generalizations my be derived from noncommutative geometry by applying e–mail:
Quantum deformations of spacetime SUSY and noncommutative superfield theory [hepth/0011053
"... We review shortly present status of quantum deformations of Poincaré and conformal supersymmetries. After recalling the κ–deformation of D=4 Poincaré supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral verti ..."
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Cited by 7 (0 self)
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We review shortly present status of quantum deformations of Poincaré and conformal supersymmetries. After recalling the κ–deformation of D=4 Poincaré supersymmetries we describe the corresponding star product multiplication for chiral superfields. In order to describe the deformation of chiral vertices in momentum space the integration formula over κ–deformed chiral superspace is proposed. 1
Spin Representations of the qPoincaré Algebra
, 2001
"... hen Algebra wird eingehend untersucht und dadurch ihr Zentrum bestimmt. Daraus k onnen zun achst die nullte Komponente und schlielich alle Komponenten des qPauliLubanskiVektor bestimmt werden. Mit dem qPauliLubanskiVektor k onnen die Algebren der SpinSymmetrie, die kleinen Algebren, berechnet ..."
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Cited by 7 (2 self)
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hen Algebra wird eingehend untersucht und dadurch ihr Zentrum bestimmt. Daraus k onnen zun achst die nullte Komponente und schlielich alle Komponenten des qPauliLubanskiVektor bestimmt werden. Mit dem qPauliLubanskiVektor k onnen die Algebren der SpinSymmetrie, die kleinen Algebren, berechnet werden, sowohl f ur den massiven als auch den masselosen Fall. Irreduzible SpinDarstellungen der qPoincareAlgebra werden konstruiert. Zun achst werden Darstellungen in einer physikalisch interpretierbaren Drehimpuls Basis berechnet. Die Berechnungen werden dabei durch die Verwendung des qWignerEckartTheorems stark vereinfacht. Anschlieend wird gezeigt, wie Darstellungen durch die Methode der Induktion gewonnen werden k onnen. Ausgehend von einer darstellungstheoretischen Interpretation von Wellengleichungen werden schlielich freie qrelativistische Wellengleichungen bestimmt. Dazu werden zun achst allgemeine Betrachtungen zu qLorentzSpinoren, konjugierten Spinoren und dem Verh altn
The classical HomYangBaxter equation and HomLie bialgebras
, 905
"... Abstract. Motivated by recent work on HomLie algebras and the HomYangBaxter equation, we introduce a twisted generalization of the classical YangBaxter equation (CYBE), called the classical HomYangBaxter equation (CHYBE). We show how an arbitrary solution of the CYBE induces multiple infinite ..."
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Cited by 6 (4 self)
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Abstract. Motivated by recent work on HomLie algebras and the HomYangBaxter equation, we introduce a twisted generalization of the classical YangBaxter equation (CYBE), called the classical HomYangBaxter equation (CHYBE). We show how an arbitrary solution of the CYBE induces multiple infinite families of solutions of the CHYBE. We also introduce the closely related structure of HomLie bialgebras, which generalize Drinfel’d’s Lie bialgebras. In particular, we study the questions of duality and cobracket perturbation and the subclasses of coboundary and quasitriangular HomLie bialgebras. 1.
Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists,” math.QA/0209180
"... Covariance of a quantum space with respect to a quantum enveloping algebra ties the deformation of the multiplication of the space algebra to the deformation of the coproduct of the enveloping algebra. Since the deformation of the coproduct is governed by a Drinfeld twist, the same twist naturally d ..."
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Cited by 6 (3 self)
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Covariance of a quantum space with respect to a quantum enveloping algebra ties the deformation of the multiplication of the space algebra to the deformation of the coproduct of the enveloping algebra. Since the deformation of the coproduct is governed by a Drinfeld twist, the same twist naturally defines a covariant star product on the commutative space. However, this product is in general not associative and does not yield the quantum space. It is shown that there are certain Drinfeld twists which realize the associative product of the quantum plane, quantum Euclidean 4space, and quantum Minkowski space. These twists are unique up to a central 2coboundary. The appropriate formal deformation of real structures of the quantum spaces is also expressed by these twists. 1
The HomYangBaxter equation and HomLie algebras
, 2009
"... Abstract. Motivated by recent work on HomLie algebras, a twisted version of the YangBaxter equation, called the HomYangBaxter equation (HYBE), was introduced by the author in [62]. In this paper, several more classes of solutions of the HYBE are constructed. Some of these solutions of the HYBE a ..."
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Cited by 5 (3 self)
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Abstract. Motivated by recent work on HomLie algebras, a twisted version of the YangBaxter equation, called the HomYangBaxter equation (HYBE), was introduced by the author in [62]. In this paper, several more classes of solutions of the HYBE are constructed. Some of these solutions of the HYBE are closely related to the quantum enveloping algebra of sl(2), the JonesConway polynomial, and YetterDrinfel’d modules. We also construct a new infinite sequence of solutions of the HYBE from a given one. Along the way, we compute all the Lie algebra endomorphisms on the (1 + 1)Poincaré algebra and sl(2). 1.