Canonical expansions of commutators and field products on the cone and at short distances in the universal algebra formalism

Mathematical formalism of universal algebras is used for the analysis of algebraic structure of the canonical Wilson expansions. The formalism provides the possibility of investigating the algebraic structure of the multiplication operations of quantum fields. In other approaches these operations are treated as basic structureless entities. It is shown that if the existence of the equal time commutators is assumed then the multiplication operation of two fields can be expressed via the singular factor which is not multiplication and via the two (independent, in general case) nonassociative multiplications which are nonsingular. The method developed is applicable to the case of the presence of additional singularities which are incompatible with the existence of the equal time commutators.