Non-local Lagrangian fields: Noether's theorem and Hamiltonian formalism

TL;DR

This paper extends Noether's theorem and Hamiltonian formalism to non-local Lagrangians with infinite degrees of freedom, including local cases and applications to p-adic string fields.

Contribution

It develops a generalized framework for non-local Lagrangians, unifying local and non-local cases within Hamiltonian and Noether's theorem formalisms.

Findings

Extended Noether's theorem for non-local Lagrangians

Established Hamiltonian formalism for infinite degrees of freedom

Applied formalism to p-adic open string field

Abstract

This article aims to study non-local 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.