МОДЕЛЬ ПУЛЬСИРУЮЩЕГО МАССИВНОГО ШАРА КАК ТОЧНОЕ РЕШЕНИЕ УРАВНЕНИЙ САМОВЗАИМНОЙ ГАМИЛЬТОНОВОЙ ДИНАМИКИ

We derive self-reciprocal twice-relativistic model of one-particle classical dynamics of spatially localized gravitating mass on the basis of Hamilton formalism in complexified extended 8-dimensional phase space taking into account Hibbons’ limit. Mass of particle, being varied in a finite interval, is a unique free parameter of the model. Exact spherically-symmetric solution of the model represents a pulsating massive ball with magnitudes of oscillations in x- and p-space and their frequency defined by the mass, that is connected by a universal relation to a corresponding action. The model has correct Newtonian limit and demonstrates classic analog of Schredinger’s Zitterbewegung. Canonic quantization of the model allows interpretation of self-reciprocal Born operator as quantum operator with eigenvalues of multipes of Planck mass squared. It leads to a model of Dirac oscillator for a fermion with Planck mass.