Nonlocal Lagrangian fields: Noether’s theorem and Hamiltonian formalism

Abstract

This article aims to study nonlocal Lagrangians with an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for them. In addition, we show that $n$-order local Lagrangians can be treated as a particular case, and the standard results can be recovered. Finally, this formalism is applied to the case of $p$-adic open string field.