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.

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