Nonlocal Lagrangian mechanics: Noether's theorem and Hamiltonian formalism
Abstract
Lagrangian systems with a finite number of degrees of freedom that are nonlocal 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. norder local Lagrangians can be treated as a particular case of nonlocal ones and standard results are recovered. The method is then applied to several other cases, namely two examples of nonlocal oscillators and the padic particle.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2021
 DOI:
 10.1088/17518121/ac265c
 arXiv:
 arXiv:2105.10442
 Bibcode:
 2021JPhA...54P5202H
 Keywords:

 nonlocal Lagrangians;
 Noether theorem;
 Hamiltonian formalsim;
 symplectic mechanics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 1 figure