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- W2092547589 abstract "Maxwell’s equations are universally solved when the charge and current densities are given, without reference to the transformation properties of the fields or charge density–current density four vector. However these transformation properties are generally held to be essential physical properties of the fields and the charge density–current density four-vector. They are required if the consequences of relativity are to hold. The way the fields and four-vectors transform constitutes a representation of the Poincaré group which can be reduced to the irreducible representations of that group first given by Wigner. The use of the irreducible representations corresponds to the expansion of the fields and currents into modes which have the simplest possible transformation properties. These modes can be identified as wave functions of particles of spin 1 and mass m (0⩽m<∞). We compare the solutions of Maxwell’s equations utilizing the “usual” time-dependent Green’s function and the method introduced in this paper. The solutions are identical, if we assume that the fields created by the time-dependent sources have the same initial values for the fields. Among the new results, we demonstrate the mechanism by which one can transform transverse fields for which the charge density is zero to fields that are partially longitudinal and for which the charge density source is not zero under Poincaré transformations of the space–time coordinates. We give a concrete example of a transverse current density source and one for a longitudinal current density source and show that sources lead to a mass spectrum of the photons. Longitudinal current densities always lead to noncausal (as noncausal is commonly understood) solutions for the fields." @default.
- W2092547589 created "2016-06-24" @default.
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- W2092547589 date "2004-04-02" @default.
- W2092547589 modified "2023-10-03" @default.
- W2092547589 title "The role of the irreducible representations of the Poincaré group in solving Maxwell’s equations" @default.
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- W2092547589 doi "https://doi.org/10.1063/1.1704847" @default.
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