Open quantum systems and Feynman integrals
type: Item
instance of: scholarly article
title: Open quantum systems and Feynman integrals
zbMATH Open document ID: 0638.46051
author: Pavel Exner
published in: Fundamental Theories of Physics
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 46-02
Mathematics Subject Classification ID: 81S40
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 4040598
zbMATH Keywords: unstable systems
zbMATH Keywords: open systems
zbMATH Keywords: one-parameter semigroup
zbMATH Keywords: exponential- decay law
zbMATH Keywords: pseudo-Hamiltonian
zbMATH Keywords: Feynman integral
zbMATH Keywords: problems of mmeasurement
zbMATH Keywords: broken symmetries
reviewed by: Alfred Wehrl
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4040598