Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation

Details Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation

2010-04-09

arxiv.org/abs/1004.1508v1

Physics

Mathematical Physics

Scientific paper

We study the existence and cardinality of normal geodesics of different causal types on H(eisenberg)-type quaternion group equipped with the sub-Lorentzian metric. We present explicit formulas for geodesics and describe reachable sets by geodesics of different causal character. We compare results with the sub-Riemannian quaternion group and with the sub-Lorentzian Heisenberg group, showing that there are similarities and distinctions. We show that the geodesics on H-type quaternion groups with the sub-Lorentzian metric satisfy the equations describing the motion of a relativistic particle in a constant homogeneous electromagnetic field.

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