Dynamical Similarity in Higher-Order Classical Symplectic Systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908713732800512 |
|---|---|
| author | Bell, Callum Sloan, David |
| author_facet | Bell, Callum Sloan, David |
| contents | Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of `contact reduction' leads to theories of a frictional nature, in which the physically-observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalisation to theories of higher order; detailed examples are provided, and physical implications discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical Similarity in Higher-Order Classical Symplectic Systems Bell, Callum Sloan, David Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 53D Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of `contact reduction' leads to theories of a frictional nature, in which the physically-observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalisation to theories of higher order; detailed examples are provided, and physical implications discussed. |
| title | Dynamical Similarity in Higher-Order Classical Symplectic Systems |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 53D |
| url | https://arxiv.org/abs/2504.00498 |