Markov Cosurfaces and Gauge Fields

  • S. Albeverio
  • R. Høegh-Krohn
  • H. Holden
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 26/1984)


We give a general construction of homogeneous Markov fields associated with d-1 hypersurfaces on a d-dimensional Riemannian manifold, with values in a Lie group G. In the case d = 2 these “Markov cosurfaces” coincide with pure continuum gauge fields with values in G. The constructed Markov cosurfaces have properties of the type of those postulated for Wilson loops Schwinger functions in the case of gauge fields and lead to relativistic quantum fields. The Markov cosurfaces provide an extension of Markov processes for the case where time points are replaced by d-1-dimensional hypersurfaces,and a corresponding extension of stochastic differential equations if given. The Markov cosurfaces are also shown to be obtainable from lattice models.


Wilson Loop Stochastic Differential Equation Gauge Field Markov Property Lattice Gauge Theory 


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • S. Albeverio
    • 1
  • R. Høegh-Krohn
    • 2
  • H. Holden
    • 2
  1. 1.Mathematisches InstitutRuhr-UniversitätBochum 1Deutschland
  2. 2.Mathematisk InstituttUniversitetet i OsloNorway

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