Quantum mechanics on phase space
This book represents a real breakthrough of the concept of P.O.V. measures in quantum mechanics; this concept, which was born in the sixties as a deep novelty inside Ludwig's axiomatic approach to quantum mechanics, he named ``effects'' (these roots of P.O.V. measures are lacking in the book), after a rather long breeding period is getting an increasing impact not only on foundations of quantum mechanics but also on a host of applications of quantum methods. The main point in the book is the systematic consideration of a phase-space structure, linked to symmetries and available due to the richer structure of P.O.V. measures; in this way some reconciliation of classical ideas and quantum formalism becomes possible. Most useful is the rigorous, efficient and selfconsistent presentation of the mathematical background, which makes this highly sophisticated subject, built both by functional analysis in Hilbert space and by differential geometry, accessible to non specialised readers; here many new contributes can be found. The possibile impact of these new ideas on foundations of quantum mechanics is discussed, in particular on the problems of measuring process, with wide consequences on foundations of physics; on this part of the research work mentioned in the book due to the highly controversial points treated, only the reader himself and further evolution of the whole subject can be good judges.
scientific article; zbMATH DE number 862938