Inelastic strong interactions at high energies. Annual Progress report, June 1, 1981-May 1, 1982

A method for constructing quarks and leptons from more elementary constituents having only Abelian symmetries was introduced. Seven elementary constituents imply four generations of the known quarks and leptons. All conformally invariant actions for SU(N) extended supergravity theories in superspace were written down in terms of seven basic structures. A new conformal geometry with linear gauge symmetry was found to define two natural scales by its breakdown, one of which is the Planck length and the other may be identified with the grand unification scale. A modified perturbation expansion, convergent for arbitrary positive coupling constant was introduced for the one and two-matrix models, related to the lattice versions of non-abelian gauge theories. An exactly soluble finite model for the renormalization group on quantum lattices was introduced. The critical properties of the model are similar to those of the infinite system, but the renormalization group transformations are singular in a large domain of the coupling parameters