Communications in Mathematical Physics

, Volume 129, Issue 2, pp 267–280 | Cite as

Universal Schwinger cocycles of current algebras in (D+1)-dimensions: Geometry and physics

  • Kazuyuki Fujii
  • Masaru Tanaka
Article
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Revised:

Abstract

We discuss the universal version of the Schwinger terms of current algebra (we call it the universal Schwinger cocycle) forp=3 (herep denotes the class of the Schatten idealI p , which is related to the (D+1) space-time dimensions byp=(D+1)/2) in detail, and give a conjecture of the general form of the cocycle for anyp. We also discuss the infinite charge renormalizations, the highest weight vector and state vectors forp=3. Last, we give brief comments on the problems caused by the difficulties to construct the measure of infinite-dimensional Grassmann manifolds.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Kazuyuki Fujii
    • 1
  • Masaru Tanaka
    • 2
  1. 1.Department of MathematicsYokohama City UniversityJapan
  2. 2.Department of PhysicsKyushu UniversityJapan

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