Construction of (λɸ4-σɸ2-μɸ)3 Quantum Field Models

  • Y. M. Park
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 15/1976)


This lecture is intended to introduce the audience to some constructions of theories for the boson field models in three dimensional space-time, which exhibit ultraviolet divergences. Constructive quantum field theory has developed rapidly in the past few years. The polynomial interactions in two dimensional space-time (the P (ɸ)2 models) are the best behaved models and its detailed structure is now well-known [2, 12, 16, 18, 19, 23, 24, 28, 30, 36, 37, 40]. Most of you may have already been exposed in the construction of the P(ɸ)2 model elsewhere (at least, you will have a change again in Prof. Challifour’s lecture at this school) and so I will not 42 discuss that subject. The (λɸ4-σɸ2-μɸ) interactions in three dimensional space-time (the (λɸ4-σɸ2-μɸ)3 models), which we are considering here, are the next well behaved, models. These differ from P(ɸ)2 by having ultraviolet divergences and by requiring ultraviolet mass wave functions as well as vacuum energy renormalizations [14, 15].


Field Model Lattice Approximation Cluster Expansion Uniform Bound Ultraviolet Divergence 


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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Y. M. Park
    • 1
    • 2
  1. 1.Department of Theoretical PhysicsUniversity of Bielefeld48 Bielefeld 1F.R. Germany
  2. 2.Department of MathematicsYonsei UniversitySeoulKorea

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