Smit, Jordi (2025) A Post-Newtonian view of the Harmonic Oscillator. Master's Thesis / Essay, Physics.
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Abstract
Building on the findings of de Neeling, we ask whether there exist relativistic systems that preserve the dynamics and symmetries of the classical isotropic harmonic oscillator (IHO). We find that these systems exist at all orders on-shell, and that off-shell an approximate equivalence exists up to at least 2PN order. We show there exists a canonical transformation between such systems back to the IHO. We list the required relation between the coefficients of the SO(N) invariant building blocks of the PN expansion, to preserve a proposed relativistic Fradkin tensor, and thus maintain closed and bounded orbits. We compare our findings to the 1PN expansion of a particle in a de Sitter background, and show by simulating the evolution of 3 Hamiltonians that the right relation among its coefficients indeed preserves a closed and bounded orbit.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Roest, D. and Seri, M. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 09 Sep 2025 07:24 |
| Last Modified: | 09 Sep 2025 07:24 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37001 |
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