Quantum kinematics

Details Quantum kinematics Quantum kinematics

2004-10-08

arxiv.org/abs/hep-th/0410086v1

Physics

High Energy Physics

High Energy Physics - Theory

Talk given at the Int. conference "Non-Commutative Geometry and Representation Theory in Mathematical Physics", 5-10 July, 200

Scientific paper

The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of $(N-1)$-dimensional constant curvature spaces are introduced. Part of the 4-dimensional constant curvature spaces are interpreted as the non-commutative analogs of $(1+3)$ kinematics. A different unifications of Cayley-Klein and Hopf structures in a kinematics are described with the help of permutations. All permutations which lead to the physically nonequivalent kinematics are found and the corresponding non-commutative $(1+3)$ kinematics are investigated. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length, the fundamental mass and the fundamental velocity are obtained.

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