ESSAY REVIEW Quantum Mechanics on Phase Space

In the Preface, the author states that his aim is to &present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics'. The way he realises his "rst three aims places Schroeck in the small and dedicated group of workers on the foundations of quantum mechanics who advocate the use of &positive-operator-valued measures'. His fourth aim, though, perhaps puts him in a somewhat eccentric corner of that community. The chapters are: I. Basic quantum theory and the necessity for its revision; II. Basic experiments suggest generalising quantum mechanics; III. Construction of quantum mechanics on phase space; IV. Consequences of formulating quantum mechanics on phase space; V. Foundational aspects; References; Index. The book is addressed at students and researchers alike, and appears to be a mixture between a textbook and a research monograph. Students who have taken an introductory course in quantum mechanics should be able to understand most of the physics material in Chapters I, II, and some in Chapters IV,