A mode theory for the electoweak interaction and its application to neutrino masses

A theory is proposed, in which the basic elements of reality are assumed to be something called modes. Particles are interpreted as composites of modes, corresponding to eigenstates of the interaction Hamiltonian of modes. At the fundamental level of the proposed theory, there are two basic modes only,whose spinor spaces are the two smallest nontrivial representation spaces of the SL(2,C) group, one being the complex conjugate of the other. All other modes are constructed from the two basic modes, making use of the operations of direct sum and direct product for related spinor spaces. Accompanying the construction of direct-product modes, interactions among modes are introduced in a natural way, with the interaction Hamiltonian given from mappings between the corresponding state spaces. The interaction Hamiltonian thus obtained turn out to possess a form, which is similar to a major part of the interaction Hamiltonian in the Glashow-Weinberg-Salam electroweak theory. In the proposed theory, it is possible for the second-order perturbation expansion of energy to be free from ultraviolet divergence. This expansion is used to derive some approximate relations for neutrino masses; in particular, a rough estimate is obtained for the ratio of mass differences of neutrinos, which gives the correct order of magnitude compared with the experimental result.