Affiliation:
1. University of Edinburgh
2. Boğaziçi University
3. KU Leuven
Abstract
We study free particle motion on homogeneous kinematical spacetimes of galilean type. The three well-known cases of Galilei and (A)dS–Galilei spacetimes are included in our analysis, but our focus will be on the previously unexplored torsional galilean spacetimes. We show how in well-chosen coordinates free particle motion becomes equivalent to the dynamics of a damped harmonic oscillator, with the damping set by the torsion. The realization of the kinematical symmetry algebra in terms of conserved charges is subtle and comes with some interesting surprises, such as a homothetic version of hamiltonian vector fields and a corresponding generalization of the Poisson bracket. We show that the Bargmann extension is universal to all galilean kinematical symmetries, but also that it is no longer central for nonzero torsion. We also present a geometric interpretation of this fact through the Eisenhart lift of the dynamics.
Funder
Boğaziçi Üniversitesi
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu
Subject
General Physics and Astronomy
Cited by
2 articles.
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1. Possible ambient kinematics;Journal of Mathematical Physics;2023-11-01
2. From pp-Waves to Galilean Spacetimes;Symmetry, Integrability and Geometry: Methods and Applications;2023-06-03