Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems

Abstract

A representation theory of the quantized Poincaré ($\kappa$-Poincaré) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincaré algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed.These results are used for the construction of some q-relativistic equations. The Wigner-Eckart theorem for QPA is proven.

18 pages

References in corpus (3)

• Quantum $\kappa$-Poincare in Any Dimensions
• The Quantum Deformed Dirac Equation from the k-Poincare` Algebra
• The Dirac-Coulomb Problem for the $\kappa$-Poincare Quantum Group

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• Doubly Special Relativity versus $\kappa$-deformation of relativistic kinematics
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• Quantum fields, non-locality and quantum group symmetries
• Noncommutative fields and the short-scale structure of spacetime
• Kappa-Deformations: Historical Developments and Recent Results
• Deformed discrete symmetries
• Twisting and kappa-Poincare
• Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time
• Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
• Parity at the Planck scale
• Towards constructing one-particle representations of the deformed Poincaré algebra