Nonperturbative Operator Quantization of Strongly Nonlinear Fields

At present an algebra of strongly interacting fields is unknown. In this paper it is assumed that the operators of a strongly nonlinear field can form a non-associative algebra. It is shown that such an algebra can be described as an algebra of some pairs. The comparison of presented techniques with the Green's functions method in superconductivity theory is made. A possible application to the QCD and High-T _c superconductivity theory is discussed.