Nonperturbative Operator Quantization of Strongly Nonlinear Fields

TL;DR

This paper proposes a nonperturbative operator algebra framework for strongly nonlinear fields, potentially applicable to QCD and high-temperature superconductivity, contrasting with traditional Green's function methods.

Contribution

It introduces a novel non-associative algebra approach for strongly nonlinear fields, expanding the mathematical tools beyond conventional techniques.

Findings

Algebra of strongly nonlinear fields can be represented as pairs.

Comparison with Green's functions in superconductivity theory is discussed.

Potential applications to QCD and high-Tc superconductivity are explored.

Abstract

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