Constructive Gauge Theory II

  • T. Balaban
Part of the NATO ASI Series book series (NSSB, volume 234)


These lecture notes are continuations of the lectures [1] from the previous Erice summer school. We assume that the reader is familiar with those, and we refer to them. In [1] we have described the lattice regularizations of gauge field theories, and their basic general properties. The renormalization group approach has been applied to the lattice theories, and explained in detail for the small field approximation. Within this approximation the renormalization group flow is determined by a mapping in the space of effective actions. The basic part of this mapping is the mapping of the coupling constant, obtained by solving the renormalization group equation. In these notes we discuss the complete model, including large field regions, and we use the above results in the small field regions. In fact even in the complete model the above described features of the renormalization transformations are preserved, with some modifications.


Gauge Field Renormalization Group Equation Gauge Field Theory Renormalization Group Approach Renormalization Group Flow 
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  1. [1]
    T. Balaban and A. Jaffe, Constructive guage theory, in: “Fundamental Problems of Gauge Field Theory,” G. Velo and A. Wightman, eds., Erice lectures, Plenum Press (1986).Google Scholar
  2. [2]
    T. Balaban, Renormalization group approach to lattice gauge field theories. I., Commun. Math. Phys. 109: 249–301 (1987).MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicolò, E. Olivieri, E. Presutti, and E. Scacciatelli, Ultraviolet stability in Euclidean scalar field theories, Commun. Math. Phys. 71: 95–130 (1980).ADSMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • T. Balaban
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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