Group analysis of Maxwell's equations

In this paper we write down and solve Maxwell's equations without sources when the field variables are considered as functions over the group SU ₂. 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.