Maxwell equations in any Riemannian space-time can be pre sented in spinor form on the base of the tetrad method, when the Maxwell field is described by a local -nd rank symmetrical spinor. This general co variant equation is specified in terms of cylindrical parabolic coordinates and of a corresponding diagonal tetrad. After separating the variables, we derive the system of four -st order differential equations with partial derivatives for three functions which depend on two parabolic coordinates. The mathematical task reduces to one -nd order equation with partial derivative for a main function, which determines all the remaining func tions. The solutions are constructed in terms of the confluent hyperge ometric functions. We study the properties of four types of constructed solutions - they must be continuous and single-valued in the context of vector or spinor space models. It is shown that in a space with vector structure only two variants provide correct solutions; in a spinor space, all four variants are appropriate. It is shown that the diagonalization of the helicity operator for a -rank symmetric spinor leads to the sys tem of equations which coincides with the one which emerges from the Maxwell equations, when identifying the eigenvalue with the frequency of electromagnetic solutions, σ = +ω. The eigenvalues σ = and σ = ?ω with respective to the eigenstates of the helicity operator are shown to be irrelevant.
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