On the Electron Spin Origin and Related Symmetry Aspects

We present a novel discussion of the electron spin origin, its symmetry properties and related conservation laws from a mathematical physics point of view, having put into the 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)− 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, 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.