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Open quantum systems and Feynman integrals. (English) Zbl 0638.46051
Fundamental Theories of Physics. Dordrecht-Bosten-Lancaster: D. Reidel Publishing Company, a Member of the Kluwer Academic Publishers Group. XIX, 356 p. Dfl. 160.00; $ 64.00; £40.75 (1985).
This book is a very comprehensive one. The starting point is how to describe unstable systems in the framework of quantum mechanics. This question yields the necessity of considering open systems, i.e. the Hilbert space of the system itself is a subspace of a larger space. In contradistinction to the favoured approach of statistical mechanics (namely, coupling the system to a heat bath or something else), for the description of unstable systems the “unstable” space \(H_ u\) is contained in some H and is not invariant under the time evolution. This gives rise to a one-parameter semigroup \(V_ t\) (which can be considered as a generalization of the well-known exponential-decay law). The generator of this semigroup is, in general, not self-adjoint and is called a “pseudo-Hamiltonian”. In order to calculate it, one can be Feynman integral techniques.
In Exner’s book one finds a very detailed treatment of all these problems - among others, a careful introduction to Feynman integrals, the problems of measurement, symmetries or broken symmetries, resp., etc. Every chapter is accompanied by very useful notes. The author understands his book as a bridge between mathematics and physics, and I think he is right.
Reviewer: A.Wehrl

46N99 Miscellaneous applications of functional analysis
46L30 States of selfadjoint operator algebras
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
81S40 Path integrals in quantum mechanics
46L60 Applications of selfadjoint operator algebras to physics
47D03 Groups and semigroups of linear operators