Abstract

The objective of this report is twofold. In the first place, it aims to demonstrate that a four-dimensional local U(1) gauge invariant relativistic quantum mechanical Dirac-type equation is derivable from the equations for the classical electromagnetic field. In the second place, the transformational consequences of this local U(1) invariance are used to obtain solutions of different Maxwell equations. Note added.. the second part is related to the idea of Baecklund transformations from soliton theory to generate different solutions from the same integral equation for some given nonlinear pde.