Dirac Fermion of a Monopole Pair (MP) Model of 4D Quantum Space-Time and Its Multifaceted Dynamics
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In quantum mechanics (QM), the electron of spin-charge, ±1/2 in probabilistic distribution about the nucleus of an atom is described by non-relativistic Schrödinger wave equation. Its transformation to Dirac fermion of a complex four-component spinor is incorporated into relativistic quantum field theory (QFT). The link between QM and QFT on the basis of space-time structure remains lacking without the development of a complete theory of quantum gravity. In this study, how a proposed MP model of 4D quantum space-time of hydrogen atom type is able to combine both QM and QFT into a proper perspective is explored. The electron of a point-particle and its transformation to Dirac fermion appears consistent with Dirac belt trick for the generation of superposition states of spin-charge. Center of mass reference frame relevant to Newtonian gravity is assigned to the point-boundary of the spherical model. Such a tool, though metaphysical, its multifaceted dynamics appear compatible with some basic aspects of both QM and QFT such as non-relativistic wave function and its collapse, quantized Hamiltonian, Dirac spinors, Weyl spinors, Majorana fermions and Lorentz transformation. How it could further relate to space-time geometry for a body-mass in an elliptical orbit is plotted for general relativity and a multiverse of the MP models at a hierarchy of scales is proposed for further investigations.