Algebraic Renormalization: Perturbative Renormalization, Symmetries and Anomalies

ISBN-13: 9783662140406 / Angielski / Miękka / 2013 / 138 str.

Olivier Piguet;Silvio P. Sorella

Opis

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.

Spis treści

Renormalized Perturbation Theory.- Quantum Action Principle and Ward Identities.- Yang-Mills Gauge Theories.- BRS Cohomology and Descent Equations.- Nonrenormalization Theorems.- Topological Field Theories.- The Bosonic String.

O autorze

The book provides a pedagocical and self-contained introduction to the algebraic method of renormalization in perturbative quantum field theory and is of particular interest to graduate students and researchers.

Blurb

This book provides a pedagogical and self-contained introduction to the algebraic method of renormalization in perturbative quantum field theory. This method is based on general theorems of renormalization, in particular on the quantum action principle. It allows us to treat the problems of the renormalizability and the anomalies of models with local or global symmetries in terms of the algebraic properties of classical field polynomials. Several examples (e.g. topological models) are considered in some detail. One of the main advantages of this method, beyond its simplicity, is its great power, because no particular subtraction or regularization scheme preserving the symmetries of the problem is a priori required.