Symmetries, Lagrangian and Conservation Laws for the Maxwell Equations

• Autores: Nail H. Ibragimov
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 105, Nº. 2, 2009, págs. 157-187
• Idioma: inglés
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• Resumen

  • The evolution equations of Maxwell�s equations has a Lagrangian written in terms of the electric E and magnetic H fields, but admit neither Lorentz nor conformal transformations. The additional equations ??E=0, ??H=0 guarantee the Lorentz and conformal invariance, but the resulting system is overdetermined, and hence does not have a Lagrangian. The aim of the present paper is to attain a harmony between these two contradictory properties and provide a correspondence between symmetries and conservation laws using the Lagrangian for the evolutionary part of Maxwell�s equations.