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Renormalization : Soft Anomalies

  • Olivier Piguet
  • Klaus Sibold
Part of the Progress in Physics book series (PMP, volume 12)

Abstract

The analysis of the renormalization properties performed in the preceding chapter led for all completely massive theories in the class of our examples to a satisfactory result. Of the examples containing massless particles, the Wess-Zumino model, SQED and S’QED still permitted an immediate treatment in the loop expansion, for the former two also all the desired vertex functions of operators were constructed without too severe an obstruction from the infrared region. (By this we mean that they exist for non-exceptional momenta.) For the O’Raifeartaigh model, however, we could prove the supersymmetry Wardidentity only up to an IR-anomaly and for SYM we did, because of the l/(k2)2 -problem, not even attempt to go beyond the analysis of the deep Euclidean region. In this chapter we shall attack these problems. For the O’Raifeartaigh model we shall find that the IR-anomaly can be absorbed by going over from the ħ-expansion to an expansion in √ħ In ħ. The validity of a strict Ward-identity implies then a wel1-determined mass generated by radiative corrections: a mass “sum-rule” [V.2]. For pure SYM an IR-regulator will be introduced which breaks supersymmetry, but maintains BRS-invariance. One constructs then Green’s functions of BRS-symmetric operators and shows that they are independent of the regulator and thus have also supersymmetry [V.5,6].

Keywords

Ward Identity Formal Power Series Renormalization Group Equation Vertex Function Gauge Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. V.1
    W.A. Bardeen, O. Piguet, K. Sibold, Mass generation in a normal product formulation, Phys. Lett. 72B (1977) 231ADSGoogle Scholar
  2. V.2
    O. Piguet, M. Schweda, K. Sibold, Radiative mass generation in perturbation theory and the renormalization group, Nucl. Phys. B168 (1980) 337MathSciNetADSCrossRefGoogle Scholar
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    K. Pohlmeyer, Large momentum behaviour of Feynman amplitudes, Lecture Notes in Physics No. 39, ed. H. Araki, Springer 1975Google Scholar
  4. V.4
    K. Symanzik, Massless Φ 4 theory in 4-ε dimensions, Cargèse Lectures 1973, DESY preprintGoogle Scholar
  5. V.5
    O. Piguet, K. Sibold, The off-shell infrared problem in SYM. I. Pure super Yang-Mills, Nucl. Phys. B248 (1984) 336ADSCrossRefGoogle Scholar
  6. V.6
    O. Piguet, K. Sibold, The off-shell infrared problem in SYM. II. All massless models, Nucl. Phys. B249 (1984) 396MathSciNetADSGoogle Scholar

Copyright information

© Birkhäuser Boston 1986

Authors and Affiliations

  • Olivier Piguet
    • 1
  • Klaus Sibold
    • 2
  1. 1.Département de Physique ThéoriqueUniversité de GenèveGenèveSwitzerland
  2. 2.Max-Planck-Institut für Physik und AstrophysikWerner-Heisenberg-Institut für PhysikMünchenFederal Republic of Germany

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