Quantum Deformations of Space-Time Symmetries and Interactions

TL;DR

This paper explores quantum deformations of space-time symmetries, focusing on the noncoassociative structures of the Galilei algebra and their relation to two-body interactions, with implications for covariant two-body systems.

Contribution

It introduces a noncoassociative deformation framework for the Galilei algebra and discusses its implications for two-body interactions and covariant systems.

Findings

Noncoassociative coproducts encode two-body interaction terms.

Quantum deformations modify symmetry structures in space-time.

Discussion of noninteraction theorem in quantum-deformed covariant systems.

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.