MODEL OF MASSIVE PULSATING SPHERE AS AN EXACT SOLUTION OF THE HAMILTONIAN SELF RECIPROCAL DYNAMICS EQUATIONS
Abstract
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.
About the Author
L. M. Tomilchik
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Corresponding Member, D. Sc. (Physics and Mathematics), Professor
Belarus
Corresponding Member, D. Sc. (Physics and Mathematics), Professor
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