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

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

1994-06-22

arxiv.org/abs/hep-th/9406146v1

Lett.Math.Phys. 32 (1994) 85-102

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1007/BF00739419

A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e 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.

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