This is a book about the Hilbert space formulation of quantum mechanics
and its measurement theory. It contains a synopsis of what became of the
Mathematical Foundations of Quantum Mechanics since von Neumann's
classic treatise with this title. Fundamental non-classical features of
quantum mechanics--indeterminacy and incompatibility of observables,
unavoidable measurement disturbance, entanglement, nonlocality--are
explicated and analysed using the tools of operational quantum theory.
The book is divided into four parts: 1. Mathematics provides a
systematic exposition of the Hilbert space and operator theoretic tools
and relevant measure and integration theory leading to the Naimark and
Stinespring dilation theorems; 2. Elements develops the basic concepts
of quantum mechanics and measurement theory with a focus on the notion
of approximate joint measurability; 3. Realisations offers in-depth
studies of the fundamental observables of quantum mechanics and some of
their measurement implementations; and 4. Foundations discusses a
selection of foundational topics (quantum-classical contrast, Bell
nonlocality, measurement limitations, measurement problem, operational
axioms) from a measurement theoretic perspective.
The book is addressed to physicists, mathematicians and philosophers of
physics with an interest in the mathematical and conceptual foundations
of quantum physics, specifically from the perspective of measurement
theory.
