Canonical Formalism for Lagrangians of Maximal Nonlocality

TL;DR

This paper develops a canonical formalism for maximally nonlocal Lagrangians using a Legendre transformation, extending the standard local theory to handle nonlocality with expanded implications.

Contribution

It introduces a novel canonical formalism for maximal nonlocality, adapting the Legendre transformation and deriving canonical equations similar to local theories.

Findings

Formalism successfully extends local canonical equations to nonlocal Lagrangians.

Method provides a systematic way to analyze maximally nonlocal systems.

Implications of the equations are significantly expanded compared to local cases.

Abstract

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is largely expanded.