TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.4.059
TI  - Particle dynamics on torsional galilean spacetimes
PY  - 2023/04/04
UR  - https://scipost.org/SciPostPhys.14.4.059
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 4
SP  - 059
A1  - Figueroa-O'Farrill, José
AU  - Görmez, Can
AU  - Van den Bleeken, Dieter
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.14.4.059,
	title={{Particle dynamics on torsional galilean spacetimes}},
	author={José Figueroa-O'Farrill and Can Görmez and Dieter Van den Bleeken},
	journal={SciPost Phys.},
	volume={14},
	pages={059},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.4.059},
	url={https://scipost.org/10.21468/SciPostPhys.14.4.059},
}