Quantum Physics: A Functional Integral Point of View

This first Glimm-Jaffe edition as well as the extended second edition are the only textbook treatments of the Osterwalder-Schrader axioms and reconstruction theorem. The mathematically more tractable and usually convergent Euclidean theory is obtained by Wick rotating the time coordinate axis by 90 degrees (i goes to -1) in the Feynman Path Integral so that quantities (Green function integrals) arising from its expansion become exponentially damped and convergent rather than oscillatory. Under what conditions can we get the Feynman amplitudes in Minkowskian spacetime from these Euclidean quantities. This of course is the Osterwalder-Schrader theory. A thorough grounding in functional analysis and distribution theory at the level of the Reed-Simon texts(mostly volumes 1 and 2)is needed to understand the proofs. This material has lately found application in loop quantum gravity. For this alone either edition is worth having.

People who complain that this book is uneccessarily hard to read probably have bought it for the wrong reasons, guided by its deceptive title. This is NOT a standard book on quantum mechanics via path integrals, as is the marvellous book by Feynman and Hibbs, among others. This is the bible on Constructive QFT (CQFT), the most recent of all attempts to put QFT on a sound mathematical basis, written by two of its founders. This IS hard physics AND hard math (Wiener integrals, unbounded operators, etc.).The book is remarkable because it collects the basics and most of the memorable results on CQFT: renormalizability of two and three-dimensional models, constructive gauge theory (indispensable for lattice gauge theories), relatioships with statistical mechanics, consistency of non-linear models, etc., associated with the insight that only the pioneers can give.Although the book is reasonably self-contained, it is strongly recommended to have a fair grounding on analysis, quantum mechanics and basic quantum field theory. The last part of the book (chapters 13-23) is meant for pros, requiring more maturity.Anyway, it's tough to find similar texts on this subject. The reader who is interested in this field of research and have some guts for tough mathematical physics certainly will be rewarded. This tome surely stands on its subject in the same footing that Haag's "Local Quantum Physics" on Algebraic QFT (another deceptive title).