Communications in Mathematical Physics

, Volume 135, Issue 1, pp 101–140 | Cite as

Semiclassical Yang-Mills theory I: Instantons

  • David Groisser
  • Thomas H. Parker
Article

Abstract

The partition functions of quantum Yang-Mills theory have an expansion in powers of the coupling constant; the leading order term in this expansion is called the semiclassical approximation. We study the semiclassical approximation for Yang-Mills theory on a compact Riemannian 4-manifold using geometric techniques, and do explicit calculations for the case when the manifold is the 4-sphere. This involves calculating the Riemannian measure and certain functional determinants on the moduli space of self-dual connections. The main result is that the contribution to the semiclassical partition functions coming from thek=1 connections on the 4-sphere isfinite andcalculable. We also discuss a renormalization procedure in which the radius of the 4-sphere is allowed to tend to infinity.

Keywords

Neural Network Manifold Complex System Partition Function Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • David Groisser
    • 1
  • Thomas H. Parker
    • 2
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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