Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics
@article{Spourdalakis2015NonlocalLA,
title={Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics},
author={Aris G.B. Spourdalakis and George Pappas and Panayotis A. Kalozoumis and Fotis K. Diakonos and Peter Schmelcher},
journal={arXiv: Quantum Physics},
year={2015}
}We introduce a class of non-local Lagrangians which allow for the variational derivation of non-local conser- vation laws in a self-consistent manner. The formalism developed here generalizes previous approaches, used in the context of $\mathcal{PT}$ symmetric quantum mechanics and optics in the paraxial approximation in a twofold way: firstly it is valid for a larger set of linear symmetry transforms and secondly it enables the derivation of additional non-local conservation laws for general…