Particle dynamics on torsional galilean spacetimes
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 coordina...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2023-04-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.14.4.059 |
| _version_ | 1797852549315821568 |
|---|---|
| author | José Figueroa-O'Farrill, Can Görmez, Dieter Van den Bleeken |
| author_facet | José Figueroa-O'Farrill, Can Görmez, Dieter Van den Bleeken |
| author_sort | José Figueroa-O'Farrill, Can Görmez, Dieter Van den Bleeken |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T19:36:09Z |
| format | Article |
| id | doaj.art-f121d732177d48e39fe0c06776eb5ab8 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-09T19:36:09Z |
| publishDate | 2023-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-f121d732177d48e39fe0c06776eb5ab82023-04-04T12:40:34ZengSciPostSciPost Physics2542-46532023-04-0114405910.21468/SciPostPhys.14.4.059Particle dynamics on torsional galilean spacetimesJosé Figueroa-O'Farrill, Can Görmez, Dieter Van den BleekenWe 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.https://scipost.org/SciPostPhys.14.4.059 |
| spellingShingle | José Figueroa-O'Farrill, Can Görmez, Dieter Van den Bleeken Particle dynamics on torsional galilean spacetimes SciPost Physics |
| title | Particle dynamics on torsional galilean spacetimes |
| title_full | Particle dynamics on torsional galilean spacetimes |
| title_fullStr | Particle dynamics on torsional galilean spacetimes |
| title_full_unstemmed | Particle dynamics on torsional galilean spacetimes |
| title_short | Particle dynamics on torsional galilean spacetimes |
| title_sort | particle dynamics on torsional galilean spacetimes |
| url | https://scipost.org/SciPostPhys.14.4.059 |
| work_keys_str_mv | AT josefigueroaofarrillcangormezdietervandenbleeken particledynamicsontorsionalgalileanspacetimes |