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Book review

Author(s) Zavialov, O.I.
Title Renormalized quantum field theory
Publisher Kluwer A.P
Year of publication 1990
Reviewed by Balan Vladimir

The volume represents a revised and enlarged translation of the Russian version (Nauka eds.,Moskow, 1979), and presents the mathematical aspects of renormalization theory in a rigorous and complete way.

The first part deals with renormalization on the level of individual diagrams, discussing criteria for infrared convergence, and describing different renormalization schemes. The second part is concerned with the renormalization on the level of the overall matrix elements, and contains the alternative approach to the Zimmermann normal product formalism. The author also considers in detail topics as short-distance and light-cone operator-product expansions and renormalization of gauge theories, and introduces a broad class of gauge-invariant regularization and renormalization schemes.

The book is written in a discursive style, but still its linear reading is not compulsory since an experienced reader can skip certain preliminaries, or can perform a direct access to necessary information (e.g. to chapter 5 - Renormalization of Yang-Mills Theory).

A useful guide to main references, a list of references, and a brief index of notions are also present.

The audience includes mathematicians and physicists concerned with renormalized QFT. The rigor and completness recommend this volume to individuals and libraries as a convenient investment.