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arXiv · 2508.03601

Nonlocal Mechanics

Carlos Heredia·Josep Llosa
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Abstract

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.

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Carlos Heredia, Josep Llosa. 2025-08-05. Nonlocal Mechanics. https://doi.org/10.1088/1751-8121%2Fae8b5e

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