Document Type

Publication - Article

Вывод уравнения Клейна-Гордона-Фока из первых принципов


Physics & Engineering

Date of Activity

Fall 2023


In present work, the Klein-Gordon-Fock equation is obtained from the first principles. Within this approach, there is no need to postulate the existence of wave functions as well as axiomatically introduce values of coefficients in the equation. The equation is derived on an adiabatically variable manifold, locally described by Friedman-Robertson-Walker metric and with complete electrodynamics constructed on it. In this case, transverse electromagnetic fie ld is quantized due to the adiabatic change in the metric tensor, and the Planck constant is an adiabatic invariant of the transverse electromagnetic field propagating over the adiabatically changed manifold. Following this approach, the wave functions appear in the equations in a natural way (they are eigen-functions of corresponding Sturm-Liouville problem) and these are the eigen-functions, the function of the transverse electromagnetic field is expanded in. For this reason, the axiomatic introduction of wave functions, as well as postulation of values o f the coefficients in the equation are no longer required. This makes obvious, both the physical meaning of the equation itself and quantum mechanics as well.


English version available upon request.