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Communications in Mathematical Physics

, Volume 23, Issue 1, pp 49–86 | Cite as

Small-distance-behaviour analysis and Wilson expansions

  • K. Symanzik
Article

Abstract

A previously described method to obtain the asymptotic forms of vertex functions at large momenta is, with the help of Wilson operator product expansion formulas, extended to momenta where the vertex functions of the zero-mass theory underlying the asymptotic forms are infrared singular. To obtain from asymptotic forms information on asymptotic behaviour requires assumptions on the behaviour of the zero-mass theory in the limit of infinite dilatation. One particular set of assumptions is discussed and found to pass a simple consistency test; this set of assumptions leads to power laws, or slight modifications thereof, with coupling-constant-independent exponents. The detailed discussion is given for the ф4 model.

Keywords

Neural Network Statistical Physic Complex System Asymptotic Behaviour Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • K. Symanzik
    • 1
  1. 1.Deutsches Elektronen-Synchrotron DESYHamburg

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