Double symmetry and infinite-component field theory

Abstract:
Qualitative characteristics and rigorous definitions are given to a new group theoretical approach which is called by double symmetry. The Gell-Mann-Levy s-model and supersymmetry are particular cases of the such approach. If a field theory is invariant under the primary symmetry group G, then, as a rule, its secondary symmetry play the role of an effective mechanism of selecting representations and eliminating available arbitrary parameters. This property of the secondary symmetry allows us to begin the mathematical and physical research of a theory of ISFIR-class fields not investigated before. Such fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible representations. All variants of the double-symmetric Lagrangians of free fields of the ISFIR-class are finded. The problems on the existence and the structure of nontrivial double-symmetric Lagrangians of the fermion-boson interaction and on some consequences of a spontaneous secondary-symmetry breaking are solved. It is shown, that in the theory under consideration there exists the such set of free parameter values, for which the fermion mass spectra are fully acceptable from the physical point of view and similar to the experimental mass spectra of barionic resonances.