Treffer: Towards a unified field theory for classical electrodynamics

Title:
Towards a unified field theory for classical electrodynamics
Authors:
BENCI, Vieri, FORTUNATO, Donato
Source:
Archive for rational mechanics and analysis. 173(3):379-414
Publisher Information:
Berlin; Heidelberg; New York, NY: Springer, 2004.
Publication Year:
2004
Physical Description:
print, 11 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Approximation et analyse numériques, Numerical approximation and analysis, Equations différentielles et équations aux dérivées partielles, problèmes aux valeurs limites, Ordinary and partial differential equations, boundary value problems, Domaines classiques de la physique (y compris les applications), Fundamental areas of phenomenology (including applications), Electromagnétisme; optique électronique et ionique, Electromagnetism; electron and ion optics, Electromagnétisme classique appliqué, Applied classical electromagnetism, Propagation des ondes électromagnétiques, propagation des ondes radioélectriques, Electromagnetic wave propagation, radiowave propagation, Champ vectoriel, Vector fields, Constante mouvement, Motion constant, Constante movimiento, Effet non linéaire, Non linear effect, Efecto no lineal, Electrodynamique, Electrodynamics, Electromagnétisme, Electromagnetism, Equation Maxwell, Maxwell equations, Equation dégénérée, Degenerate equation, Ecuación degenerada, Equation elliptique, Elliptic equations, Fonction convexe, Convex function, Función convexa, Fonction régulière, Smooth function, Función regular, Modélisation, Modelling, Onde solitaire, Solitary wave, Onda solitaria, 0260L
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Dipartimento di Matematica Applicata U. Dini Università degli Studi di Pisa, via Bonanno 25/b, 56126 Pisa, Italy
Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125 Bari, Italy
ISSN:
0003-9527
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=16128574
Rights:
Copyright 2004 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Physics: electromagnetism

Theoretical physics
Accession Number:
edscal.16128574
Database:
PASCAL Archive

Weitere Informationen

In this paper we introduce a model which describes the relation of matter and the electromagnetic field from a unitarian standpoint in the spirit of ideas of Born and Infeld. In this model, based on a semilinear perturbation of Maxwell equations, the particles are finite-energy solitary waves due to the presence of the nonlinearity. In this respect the matter and the electromagnetic field have the same nature. Finite energy means that particles have finite mass and this makes electrodynamics consistent with the special relativity. We analyze the invariants of the motion of the semilinear Maxwell equations (SME) and their static solutions. In the magnetostatic case (i.e., when the electric field E = 0 and the magnetic field H does not depend on time) SME are reduced to the semilinear equation ⊇ × Δ × A = f'(A), (1) where V x denotes the curl operator, f' is the gradient of a strictly convex smooth function f: R3 → R and A: R3 → R3 is the gauge potential related to the magnetic field H (H = V x A). Due to the presence of the curl operator, (1) is a strongly degenerate elliptic equation. Moreover, physical considerations impel f to be flat at zero (f(0) = 0) and this fact leads us to study the problem in a functional setting related to the Orlicz space LP + Lq. The existence of a nontrivial finite-energy solution of (1) is proved under suitable growth conditions on f. The proof is carried out by using a suitable variational framework related to the Hodge splitting of the vector field A.