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Electrodynamics in terms of functions over the groupSU(2). I. The equation of the vector potential

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Abstract

This is the first in a series of papers in which a method of harmonic analysis in terms of functions over the groupSU(2) is applied to the description of interaction between matter and the electromagnetic field. Carmeli'sSU(2) formulation of Maxwell's equations is extended to anSU(2) formulation of the equations for the electromagnetic vector potential. The four functions which describe the vector potential are expanded in a generalized Fourier series [SU(2) harmonic analysis] and the equations for the coefficients are derived. These equations are not independent of each other, but in a given order they can be solved consecutively one at a time.

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Supported in part by the Sloan Foundation and the Colgate Research Council.

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Barut, A.O., Malin, S. Electrodynamics in terms of functions over the groupSU(2). I. The equation of the vector potential. Found Phys 5, 375–386 (1975). https://doi.org/10.1007/BF00708884

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Keywords

  • Fourier
  • Electromagnetic Field
  • Harmonic Analysis
  • Fourier Series
  • Vector Potential