Quantum deformation of space-time symmetries and interactions |
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Authors: | Jerzy Lukierski Peter C Stichel |
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Institution: | (1) Institute of Theoretical Physics, University of Wroc aw, pl. Maxa Borna 9, 50-203 Wroc aw, Poland.;(2) Faculty of Physics, University of Bielefeld, Postfach 8640, Universitätsstrasse, 4800 Bielefeld, Germany. |
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Abstract: | We discuss quantum deformations of Lie algebra as described by the noncoassociative modification of its coalgebra structure. We consider for simplicity the quantum D = 1 Galilei algebra with four generators: energy H, boost B, momentum P and central generator M (mass generator). We describe the nonprimitive coproducts for H and B and show that their noncocommutative and noncoassociative structure is determined by the two-body interaction terms. Further we consider the case of physical Galilei symmetry in three dimensions. Finally we discuss the noninteraction theorem for manifestly covariant two-body systems in the framework of quantum deformations of D = 4 Poincaré algebra and a possible way out. |
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