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Invariant decomposition of the retarded electromagnetic field.
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The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.
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GRAELLS, J., MARTÍN, C., CODINA I VIDAL, Josep ma. (josep maria). Invariant decomposition of the retarded electromagnetic field.. _Journal of Mathematical Physics_. 1985. Vol. 26, núm. 8, pàgs. 2024-2029. [consulta: 28 de gener de 2026]. ISSN: 0022-2488. [Disponible a: https://hdl.handle.net/2445/24568]