Second quantization of classical nonlinear relativistic field theory

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 \(\hat \Phi \) is obtained. The construction of asymptotic local relativistic fields \(\hat \Phi _{in} \) and \(\hat \Phi _{out} \) associated with \(\hat \Phi \) is also given.