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

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