Quantum Theory

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics.

The Emergent Multiverse presents a striking new account of the "many worlds" approach to quantum theory. The point of science, it is generally accepted, is to tell us how the world works and what it is like.

issues raised by quantum theory, a topic not very popular during his student days at Queen's University, Belfast. Apparently, John Bell, who had been interested in the Bohr-Einstein dialogue, always took the position of Albert Einstein on philosophical issues. He also felt that a completion of quantum mechanics using so-called "hidden variables" would be highly desired, as it would help to regain a realistic and objective picture of the world. That way, Bell hoped one would be able to arrive at a physics where "measurement" would not play such a central role as in the Copenhagen interpretation of quantum mechanics.

Operational Quantum Theory I is a distinguished work on quantum theory at an advanced algebraic level. The classically oriented hierarchy with objects such as particles as the primary focus, and interactions of these objects as the secondary focus is reversed with the operational interactions as basic quantum structures.

This book concentrates on the famous Grothendieck inequality and the continued search for the still unknown best possible value of the real and complex Grothendieck constant (an open problem since 1953). It describes in detail the state of the art in research on this fundamental inequality, including Krivine's recent contributions, and sheds light on related questions in mathematics, physics and computer science, particularly with respect to the foundations of quantum theory and quantum information theory. Unifying the real and complex cases as much as possible, the monograph introduces the reader to a rich collection of results in functional analysis and probability. In particular, it includes a detailed, self-contained analysis of the multivariate distribution of complex Gaussian random vectors. The notion of Completely Correlation Preserving (CCP) functions plays a particularly important role in the exposition.

The principal intent of this monograph is to present in a systematic and self-con­ tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory.