Quaternion-valued integral representations of time-harmonic electromagnetic and spinor fields

Close relationship of solutions of the equation system, coinciding with the Maisul-Teodoresku system (the spatial analogue of the Coshi-Riemann equations), with time-harmonic solutions of the Maxwell-Dirac equations is shown. The analogues of the Coshi integral formula, the Sochatski formulae as well as solutions of boundary tasks, analoguous to the tasks of analytical continuance in the theory of complex variable functions, are obtained. 12 refs