Second quantization of classical nonlinear relativistic field theory - Part II. Construction of relativistic interacting local quantum field

The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field {Mathematical expression} is obtained. The construction of asymptotic local relativistic fields {Mathematical expression} and {Mathematical expression} associated with {Mathematical expression} is also given.