Dirac Fermion of a Monopole Pair (MP) Model of 4D Space-Time and Its Wider Implications

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Abstract

In quantum mechanics (QM), the electron of spin-charge, ±1/2 in probabilistic distribution about a 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) based on Dirac theory. The link between QM and QFT on the basis of space-time structure remains lacking without the development of a proper, complete theory of quantum gravity. In this study, how a proposed MP model of 4D space-time mimicking 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 while sustaining unitarity of spin-charge and wave-particle duality with center of mass reference frame relevant to Newtonian gravity assigned to the point-boundary of the spherical model. Such a tool appears dynamic and is compatible with basic aspects of both QM and QFT such as non-relativistic wave function and its collapse, quantized Hamiltonian, Dirac spinors, Weyl spinors, Marjorana fermions and Lorentz transformation. How all these relate to space-time curvature for an elliptical orbit without invoking a framework of space-time fabric is plotted for general relativity and a multiverse of the MP models at a hierarchy of scales is proposed for further investigations.

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