Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.03601 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915591198081024 |
|---|---|
| author | Heredia, Carlos Llosa, Josep |
| author_facet | Heredia, Carlos Llosa, Josep |
| contents | We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and a generalized Noether theorem, we define the canonical momenta and energy. Moreover, we construct a (pre)symplectic form on the kinematic space, and show that its restriction to the phase space (by implementing the constraints) yields a true (pre)symplectic structure encoding the dynamics. Three examples -- a finite nonlocal oscillator, the fully nonlocal Pais-Uhlenbeck model, and a delayed harmonic oscillator -- demonstrate how phase space and the Hamiltonian emerge without explicitly solving the Euler-Lagrange equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal Mechanics Heredia, Carlos Llosa, Josep High Energy Physics - Theory Mathematical Physics We introduce a Hamiltonian framework for nonlocal Lagrangian systems without relying on infinite-derivative expansions. Starting from a (trajectory-based) variational principle and a generalized Noether theorem, we define the canonical momenta and energy. Moreover, we construct a (pre)symplectic form on the kinematic space, and show that its restriction to the phase space (by implementing the constraints) yields a true (pre)symplectic structure encoding the dynamics. Three examples -- a finite nonlocal oscillator, the fully nonlocal Pais-Uhlenbeck model, and a delayed harmonic oscillator -- demonstrate how phase space and the Hamiltonian emerge without explicitly solving the Euler-Lagrange equations. |
| title | Nonlocal Mechanics |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2508.03601 |