Extension of the Standard CD Algebra in the Axiomatic Approach for Spinor Field and Fermi–Bose Duality

Abstract

The exclusive representations of the extended (29-dimensional) real-number Clifford–Dirac algebra are constructed for the spinor field. In the canonical Foldy–Wouthuysen representation for a \({e^-e^+}\)-dublet these representations contain physically justified on equal footing and conserved in time fermion and boson spins, and the canonical equation of motion for a dublet coincides with the quantum mechanical equation in the Hilbert space \({L_2({\mathcal R}^3)\times {\mathcal C}^4 \equiv H^{3,4}}\) with definite metrics. In \({H^{3,4}}\) the experimentally observed dublet energy is always positive. The Fermi and Bose spins define sets of both equal status Fermi and Bose states, which univocally elucidate the physical content of the Fermi–Bose (FB)-dualism of the \({e^-e^+}\) microobject. We briefly review the ad hoc boson object in the same space as partner of the \({e^-e^+}\)-dublet and treat issues, related to its BF-dualism. The mathematical correctness of the technique is acquired by the application of the simplified variant of the axiomatic approach (A-approach) to the spinor field.