Algebraic Renormalization

1. Front Matter

   Pages I-IX

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2. Introduction

   Pages 1-2

3. Renormalized Perturbation Theory

   Pages 3-20

4. Quantum Action Principle and Ward Identities

   Pages 21-36

5. Yang-Mills Gauge Theories

   Pages 37-57

6. BRS Cohomology and Descent Equations

   Pages 59-79

7. Nonrenormalization Theorems

   Pages 81-92

8. Topological Field Theories

   Pages 93-115

9. The Bosonic String

   Pages 117-127

10. Back Matter

    Pages 129-134

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The idea of this book originated from two series of lectures given by us at the Physics Department of the Catholic University of Petr6polis, in Brazil. Its aim is to present an introduction to the "algebraic" method in the perturbative renormalization of relativistic quantum field theory. Although this approach goes back to the pioneering works of Symanzik in the early 1970s and was systematized by Becchi, Rouet and Stora as early as 1972-1974, its full value has not yet been widely appreciated by the practitioners of quantum field theory. Becchi, Rouet and Stora have, however, shown it to be a powerful tool for proving the renormalizability of theories with (broken) symmetries and of gauge theories. We have thus found it pertinent to collect in a self-contained manner the available information on algebraic renormalization, which was previously scattered in many original papers and in a few older review articles. Although we have taken care to adapt the level of this book to that of a po- graduate (Ph. D. ) course, more advanced researchers will also certainly find it useful. The deeper knowledge of renormalization theory we hope readers will acquire should help them to face the difficult problems of quantum field theory. It should also be very helpful to the more phenomenology oriented readers who want to famili- ize themselves with the formalism of renormalization theory, a necessity in view of the sophisticated perturbative calculations currently being done, in particular in the standard model of particle interactions.

• Anomalien
• Anomalies
• BRS
• Cohomolgy
• Cohomologie
• Eichtheorien
• Gauge Theories
• Quantenfeldtheorie
• Renormalization
• Renormierung
• Symmetries
• homology
• quantum field theory

• Département de Physique Théorique, Université de Genève, Genève 4, Switzerland

  Olivier Piguet

• Centro Brasileiro de Pesquisas Fisicas, Urca Rio de Janeiro, Brazil

  Silvio P. Sorella

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