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arXiv · 1510.00548

Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics

A. G. B. Spourdalakis·G. Pappas·P. A. Kalozoumis·F. K. Diakonos·P. Schmelcher
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Abstract

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 higher dimensional wave mechanical systems.

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A. G. B. Spourdalakis, G. Pappas, P. A. Kalozoumis, F. K. Diakonos, P. Schmelcher. 2015-10-02. Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics. https://arxiv.org/abs/1510.00548

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