2025/08/05 by Carlos Heredia, Carlos Heredia Pimienta, Josep Llosa +2
Physics and Astronomy · #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian optics #Hamiltonian system #Harmonic oscillator #Kinematics #Lagrangian #Noether's theorem #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Phase space #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.1088/1751-8121/ae8b5e
published in Journal of Physics A Mathematical and Theoretical 59(29), 295207 (Institute of Physics)
openalex publication_date 2026/07/15 · openalex created_date 2026/07/16 · openalex updated_date 2026/08/05
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 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.