Quantum Deformations of Space-Time Symmetries and Interactions

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 $D=4$ \poin algebra and a possible way out.

LaTeX, 10 pages

References in corpus (1)

• The classical basis for $\kappa$-deformed Poincaré (super)algebra and the second $\kappa$-deformed supersymmetric Casimir

Cited by in corpus (1)

• On Supergroups with Odd Clifford Parameters and Supersymmetry with Modified Leibniz Rule