Semi-Differential Operators and the Algebra of Operator Product Expansion of Quantum Fields

We introduce a symmetric operad whose algebras are the Operator Product Expansion (OPE) Algebras of quantum fields. There is natural classical limit for over this and they commutative associative with derivations. The latter In paper we completely develop our approach to models fields, which come from vertex in higher dimensions. However, OPE can be extended general fields even curved space-time. notion operations based on new semi-differential operators. linear operators Gamma M N between two modules algebra A, such that every m belonging assignment "a maps Gamma(a.m)" differential operator A usual sense. residue meromorphic function at its pole an example operator.