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Quantum Field Theory in Terms of Random Walks and Random Surfaces

  • Jürg Fröhlich
Part of the NATO ASI Series book series (NSSB, volume 115)

Abstract

In these notes I wish to summarize some recent developments in relativistic quantum field theory (RQFT) which have led to the idea that some class of RQFT in the Euclidean description, i.e. at imaginary time, should be viewed as classical statistical mechanics of interacting random walks and random surfaces. Put differently, the construction of many models of RQFT is a problem in stochastic geometry. We shall see that random walks describe fluctuations of matter degrees of freedom - quarks, leptons, Higgs particles - while random surfaces describe fluctuations of the “field of force”, i.e. of the degrees of freedom of gauge fields. More precisely, random surfaces describe the fluctuations of the (chromo-electric) flux sheets of gauge theories in the confinement phase.

Keywords

Gauge Theory Continuum Limit Lattice Gauge Theory Random Surface Classical Statistical Mechanic 
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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  1. 1.Theoretical PhysicsETH-HönggerbergZürichSwitzerland

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