Title: A mode theory for the electoweak interaction and its application to neutrino masses,
Abstract: 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.