Physics of Currents and Potentials IV. Dirac Space and Dirac Vectors in the Quantum Relativistic Theory (original) (raw)
There has been presented an attempt to transfer the fundamental ideas of physics of continual currents and potentials, described in the previous articles of this series [1], [2], [3], from the classical theory to the quantum relativistic theory. The concept of multidimensional Dirac space, which should contain wave equations of the relativistic quantum theory, has been introduced. Dirac space dimension d is determined by Yang-Mills multiplicity of the sector of physics: d = 8 for the singlet (quantum electrodynamic states); d = 20 for the two-sector singlet-triplet states; d = 52 for the three-sector singlet-triplet-octuplet states. It has been shown that the quantum relativistic state can not be described by the unique wave function (four-component Dirac vector). Singlet states are described by a pair of Dirac vectors, two-sector singlet-triplet states are described by four Dirac vectors, eight Dirac vectors are necessary for description of the three-sector singlet-triplet-octuplet states. It has been shown that the necessity to consider the Riemann curvature of space causes additional difficulties in the process of construction of the quantum relativistic theory.
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