Hamiltonian formulation of the Klein-Gordon-Maxwell equations
type: Item
instance of: scholarly article
title: Hamiltonian formulation of the Klein-Gordon-Maxwell equations
zbMATH Open document ID: 1221.35003
DOI: 10.4171/RLM/590
author: Vieri Benci
author: Donato Fortunato
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2011-08-02T00:00:00Z
review text: The nonlinear Klein-Gordon-Maxwell equations (NKGM) provide models for the interaction between the electromagnetic field and matter. The relevance of NKGM relies on the fact that they are the ``simplest'' gauge theory which is invariant under the group of Poincaré. These equations present the interesting phenomenon of solitons. In this article, the writers show that NKGM present an Hamiltonian structure and hence they can be written as equations of the first order in \(t\). This fact is not trivial since the Lagrangian does not depend on \(\partial_{t}\varphi\) (see sec. 3.3) and a suitable analysis of its structure is necessary. In the last section, the authors recollect a recent result which states the existence of solitons by using the particular structure of the Hamiltonian.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 35Q61
zbMATH DE Number: 5935218
zbMATH Keywords: Maxwell equations
zbMATH Keywords: Klein-Gordon equation
zbMATH Keywords: Q-balls
zbMATH Keywords: hylomorphic solitons
zbMATH Keywords: gauge theory
reviewed by: Ömer Kavaklioglu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5935218