Vacuum Structure in QCD

  • A. Patrascioiu
  • E. Seiler
Part of the NATO ASI Series book series (NSSB, volume 255)


It is shown that nonlinear σ models in two dimensions and gauge theories in any dimension are characterized by the absence of an ordered state. This situation renders perturbation theory at best suspicious. The outline of a proof that the 0(N) N ≥ 2 nonlinear σ models in 2D possess a phase characterized by algebraic decay of correlations is presented. The argument is based upon an analysis of the percolating properties of certain clusters. The result implies that the true Callan Symanzik ß-function of such models is vanishing, in contradiction to the well-known predictions of asymptotic freedom obtained in perturbation theory for N > 2. The connection between topological properties and the phase structure of such models is also addressed.


Gauge Theory Asymptotic Freedom Nonabelian Gauge Theory Nonrelativistic Quantum Mechanic Algebraic Decay 
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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • A. Patrascioiu
    • 1
  • E. Seiler
    • 2
  1. 1.Physics Department and Center for the Study of Complex SystemsUniversity of ArizonaTucsonUSA
  2. 2.Max-Planck-Institut für PhysikAstrophysik Werner Heisenberg Institut für PhysikMunichFederal Republic of Germany

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