First step towards the derivation of Klein-Gordon-Fock equation from first principles

Models, unlike theories, are based on axioms, which hinder their physical meanings in many cases. This is one of the reasons why the discussions of the physical foundations of quantum mechanics have been going on unsatisfactorily for decades. To rebuild the theories on more rigorous foundations, physicists ought to go as far back as possible to write out the basic equations of quantum physics. In this work, as an example, the Klein-Gordon-Fock equation is obtained from first principles. An adiabatically varying manifold described locally by the time-dependent Robertson-Walker metric is considered. Under these conditions, the eigenfunctions of the Sturm-Liouville problem are series expansions of the functions of free electromagnetic field, and, instead of being introduced axiomatically, the wave function appears naturally with its probabilistic interpretation. Some consequences and applications are presented.