Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian formalism

Abstract

We study Lagrangian systems with a finite number of degrees of freedom that are non-local in time. We obtain an extension of Noether theorem and Noether identities to this kind of Lagrangians. A Hamiltonian formalism is then set up for this systems. $n$-order local Lagrangians can be treated as a particular case and the standard results for them are recovered. The method is then applied to several other cases, namely two examples of non-local oscillators and the p-adic particle.

1 figure

References in corpus (1)

• Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Cited by in corpus (2)

• Non-local scalar fields in static spacetimes via heat kernels
• Infinite-derivative linearized gravity in convolutional form