Group Analysis of Maxwell's Equations

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Abstract
In this paper we write down and solve Maxwell's equations without sources when the field variables are considered as functions over the group SU2. A Hilbert space is then constructed out of the field functions. An expansion of the field functions in terms of the matrix elements of the irreducible representation of SU2 is shown to reduce the problem of solving Maxwell's equations to that of solving one partial differential equation with two variables. A Fourier transform reduces this equation into an ordinary differential equation which is identical to the partial‐wave equation obtained from the Schrödinger equation with zero potential. The analogy between the mathematical method used in this paper in relation to the group SU2 and the Fourier transform in relation to the additive group of real numbers is pointed out.

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