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.

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References in corpus (12)

• Towards singularity and ghost free theories of gravity
• Tachyon Dynamics in Open String Theory
• Bouncing Universes in String-inspired Gravity
• Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons
• On the Nonlinear Dynamical Equation in the p-adic String Theory
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Tachyon Condensation and Brane Descent Relations in p-adic String Theory
• Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity
• A Canonical Formalism For Lagrangians With Nonlocality Of Finite Extent
• Towards multifractional calculus
• Functional Lagrange formalism for time-non-local Lagrangians
• Energy-momentum tensor for the electromagnetic field in a dispersive medium as an application of Noether theorem

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• Ghost-free infinite-derivative dilaton gravity in two dimensions
• Nonlocal Lagrangian fields and the second Noether theorem. Non-commutative $U(1)$ gauge theory
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox