Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems
Henri Ruegg, Valeriy N. Tolstoy
Abstract
A representation theory of the quantized Poincaré (κ-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.
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