Communications in Mathematical Physics

, Volume 48, Issue 3, pp 291–311 | Cite as

Second quantization of classical nonlinear relativistic field theory

Part II. Construction of relativistic interacting local quantum field
  • T. Bałaban
  • K. Jezuita
  • R. Rączka


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.


Neural Network Statistical Physic Field Theory Vector Space Complex System 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • T. Bałaban
    • 1
  • K. Jezuita
    • 2
  • R. Rączka
    • 2
  1. 1.Institute of MathematicsUniversity of WarsawWarsawPoland
  2. 2.Institute of Nuclear ResearchWarsawPoland

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