
Author(s)  Horuzhy, S.S. 

Title  Introduction to algebraic quantum field theory 
Publisher  Kluwer A.P 
Year of publication  1990 
Reviewed by  Balan Vladimir 
The book is a translation of the Russian version published in 1986, presenting for the first time a systematic introduction to the algebraic approach to quantum field theory.
The advances in the subject are closely reflected in the structure of the contents. Thus, chapter 1 presents the axioms and many of their wellknown consequences, and deals with the axiomatic theory of local observable algebras; since without the field concepts the developed theory is incomplete, chapter 2 shows that by means of superselection rules, the fields are reconstructed from observables, making hence the transition from the formalism of observables to the fieldtheoretic description; chapter 3 presents the formalism of field algebras (the algebras of Wightman fields, first unbounded operator algebras, the Neumann field algebras and local algebras of free and generalised free fields).
An appendix contains problems of constructing algebraic gauge quantum field theory. The bibliography encloses the main original results in algebraic QFT, and is followed by a detailed subject ndex.
The mathematical background of the reader has to include the theory of algebras, and the physical one includes the general QFT and Wightman's axiomatic theory.
The book is written in a rigorous style, and can be recommended to mathematicians and mathematical physicists interested in the foundations and mathematical methods of QFT; it represents a useful and valuable aquisition for individuals and libraries as well.