Non-local Lagrangian mechanics: Noether’s theorem and Hamiltonian formalism

@article{Heredia2021NonlocalLM,
  title={Non-local Lagrangian mechanics: Noether’s theorem and Hamiltonian formalism},
  author={Carlos Heredia and Josep Llosa},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
  • Carlos HerediaJ. Llosa
  • Published 21 May 2021
  • Mathematics, Physics
  • Journal of Physics A: Mathematical and Theoretical
Lagrangian systems with a finite number of degrees of freedom that are non-local in time are studied. We obtain an extension of Noether’s theorem and Noether identities to this kind of Lagrangians. A Hamiltonian formalism has then been set up for these systems. n-order local Lagrangians can be treated as a particular case of non-local ones and standard results are recovered. The method is then applied to several other cases, namely two examples of non-local oscillators and the p-adic particle. 

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