Spinorial analysis and physical properties of fermions

Abstract

We study the formalism of covariant differentiation of a spinor field in a space of affine connection with an invariant metric. We find the most general formula for the coefficients of spinorial connection Γα consistent with the fundamental relationship between the space and spin (γαγβ + γβγα = 2gγαβ), and which is a generalization of the formula for the Fock-Ivanenko coefficients. The obtained formula contains additional terms describing the interaction between the spinor field and the scalar field, the vector field Aα, and the pseudovector field\(\mathop {\text{A}}\limits^ \vee _\alpha \) (presumably, the pseudotrace of the spacetime torsion). The existence of these interaction terms also follows from the analysis of spinor fields from the gauge-theoretical point of view. We show that the interaction between the spinor and pseudovector fields found in this paper substantially modifies the electrodynamics of spinor fields. As a result, the combined system of equations describing the dynamics of the vector (electromagnetic) and pseudovector fields is, unlike the Maxwell equations, symmetric with respect to the right-hand sides (sources). The source for the field strength tensor of the field comples Aα and\(\mathop {\text{A}}\limits^ \vee _\alpha \) is the vector current of the spinor field ¯gyγαψ, while the source for the dual field strength tensor is the pseudovector current of the spinor field ¯ψγαγ5ψ. It is suggested that the obtained interaction between the spinor and the scalar and pseudovector fields plays a role on a deeper level of matter structure —in quark and preon (subquark) systems.