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Communications in Mathematical Physics

, Volume 83, Issue 2, pp 213–242 | Cite as

On the regular holonomic character of theS-matrix and microlocal analysis of unitarity-type integrals

  • Takahiro Kawai
  • Henry P. Stapp
Article

Abstract

The previously proved results that every analytically renormalized Feynman integral is a regular holonomic function suggests that theS-matrix should be locally expressible as an infinite sum of regular holonomic functions. A regularity propertyR is formulated that expresses the condition that theS-matrix be locally expressible near each physical pointp as a convergent sum of regular holonomic functions, with each term enjoying some of the regularity properties of a corresponding Feynman integral. This propertyR holds at every physical pointp that has yet been analyzed by the methods of axiomatic field theory orS-matrix theory. Some analyticity properties of unitarity-type integrals are then examined under the assumption that theS-matrix satisfies propertyR and a weak integrability condition. These results rest heavily on some recently proved properties of regular holonomic functions.

Keywords

Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Takahiro Kawai
    • 1
    • 2
  • Henry P. Stapp
    • 3
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  3. 3.Lawrence Berkeley LaboratoryUniversity of CaliforniaBerkeleyUSA

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