Universal matrix form of the joint field equation in the standard electroweak interaction theory (Q584350)

The nonlinear equations for interacting (self-interacting) fields in the Glashow-Salam-Weinberg gauge theory of electroweak interactions are formulated in universal matrix form (Fedorov, 1960; Okubo, Tosa, 1979) as a single first-order equation with nonlinearities of second power only. The matrix formulation of the corresponding Lagrange density is also presented. The obtained matrices are expressed in terms of the basic elements (with projective properties) of complete matrix (quadratic and cubic) algebras, defined by means of generalized Kronecker symbols (Bogush, Fedorov, 1968) in the joint field function space of the leptons, quarks, gauge bosons and Higgs particles. The general approach which allows to realize such one procedure and has been applied previously in gravity theory, general non-Abelian gauge field theory, scalar and spinor quantum electrodynamics, quantum chromodynamics as well as in supersymmetric and supergauge field theories is described.