Some Remarks on the Electron Spin SU(2) × SU(2)-Symmetry Structure and the Related Ground State Properties

We present a novel description of the electron spin origin, its symmetry properties and related conservation laws from mathematical physics point of view, having put into background the algebraic description of the corresponding physically observed representations. There is analyzed in detail the spin structure and its crucial dependence on the $$SU(2) \times SU(2)$$ -symmetry properties of the related representations of the basic Clifford algebra, generated by creation-annihilation operators on the Fock space and the related chirality symmetry of the Pauli spin operators. Based on the conservation law of the spin projection on the electron momentum there is proposed a novel derivation of the Dirac Hamiltonian operator, whose Lorentz invariance is naturally related to that of the fundamental Maxwell equations, whose quanta are carriers of interaction between electrons. The related electron ground state properties are treated in the framework of the extended $$\left( {SU(2) \times SU(2)} \right) \times U(1)$$ gauge group symmetry, applied to a vacuum matter bispinor field, giving rise to dubbed $${{W}^{ \pm }}$$ - and $$Z$$ -boson fields and producing no Higgs boson field. There is also discussed the self-interaction phenomenon within the quantum renormalized Lorentz constraint on a suitably reduced Fock space within the many-temporal Fock and Feynman proper time paradigms.