Dynamical theory of subconstituents based on ternary algebras

Abstract

We propose a dynamical theory of possible fundamental constituents of matter. Our scheme is based on (super) ternary algebras which are building blocks of Lie (super) algebras. Elementary fields, called "ternons," are associated with the elements of a (super) ternary algebra. Effective gauge bosons, "quarks," and "leptons" are constructed as composite fields from ternons. We propose two- and four-dimensional (super) ternon theories whose structures are closely related to $\mathrm{C}{\mathrm{P}}_N$ and Yang-Mills theories and their supersymmetric extensions. We conjecture that at large distances (low energies) the ternon theories dynamically produce effective gauge theories and thus may be capable of explaining the present particle-physics phenomenology. Such a scenario is valid in two dimensions.