Comparison of the Algorithmic and Axiomatic Approaches to the Construction of Quantum Field Theory

Abstract

Two possibilities of the quantum theory construction, indicated by Feynman, are examined. The special features of the structure of the Standard Model (SМ) are enumerated, which attest to the fact that SM is not an axiomatic, but an algorithmic theory. Deficiencies of SM and possibilities of overcoming these deficiencies are indicated. The structure of the nonlinear quantum field theory (NQFT) as an axiomatic theory, which makes it possible to overcome deficiencies in the Standard Model, is presented.