Contents 1. A glimpse of Quantum Probability Theory and of a Quantum Theory of Experiments 1 1.1. Might quantum probability theory be a subfield of (classical) probability theory? 3 1.2. The quantum theory of experiments 7 1.3. Organization of the paper 9 Acknowledgements 10 2. Models of Physical Systems 10 2.1. Some basic notions from the theory of operator algebras 11 2.2. The operator algebras used to describe a physical system 13 2.3. Potential properties, information loss and possible events 15 3. Classical ("realistic") models of physical systems 18 3.1. General features of classical models 18 3.2. Symmetries and time evolution in classical models 19 3.3. Probabilities of histories, realism and determinism 20 4. Physical systems in quantum mechanics 21 4.1. Complementary possible events do not necessarily exclude one another 21 4.2. The problem with conditional probabilities 23 4.3. Dephasing/Decoherence 24 4.A. Appendix to Section 4. Remarks on positive operator-valued measures, (POVM) 27 5. Removing the veil: Empirical properties of physical systems in quantum mechanics 28 5.1. Information loss and entanglement 29 5.2. Preliminaries towards a notion of "empirical properties" of quantum mechanical systems 30 5.3. So, what are "empirical properties" of a quantum-mechanical system? 32 5.4. When does an observation or measurement of a physical quantity take place? 34 5.5. Generalizations and summary 37 5.6. Non-demolition measurements 38 5.A. Appendix to Section 5 42 References 44 J. FRÖHLICH AND B. SCHUBNELpotential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).The "foundations of quantum mechanics" represent a notoriously thorny and enigmatic subject. Asking twenty-five grown up physicists to present their views on the foundations of quantum mechanics, one can expect to get the following spectrum of reactions 1 : Three will refuse to talk -alluding to the slogan "shut up and calculate" -three will say that the problems encountered in this subject are so difficult that it might take another 100 years before they will be solved; five will claim that the "Copenhagen Interpretation", [73], has settled all problems, but they are unable to say, in clear terms, what they mean; three will refer us to Bell's book [8] (but admit they have not understood it completely); three confess to be "Bohmians" [24] (but do not claim to have had an encounter with Bohmian trajectories); two claim that all problems disappear in the Dirac-Feynman path-integral formalism [22,28]; another two believe in "many worlds" [27] but make their income in our's, and two advocate "consistent histories" [40]; two swear on QBism [35], (but have never seen "les demoiselles d'Avignon"); two are convinced that the collapse of the wave function [37] -spontaneous or not -is fundamental; and one thinks that one must appeal to quantum gravity to a...

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Abstract. A simple model of an atom interacting with the quantized electromagnetic field is studied. The atom has a finite mass m, finitely many excited states and an electric dipole moment, d0 = −λ0 d, where d i = 1, i = 1, 2, 3, and λ0 is proportional to the elementary electric charge. The interaction of the atom with the radiation field is described with the help of the Ritz Hamiltonian, − d0 · E, where E is the electric field, cut off at large frequencies. A mathematical study of the Lamb shift, the decay channels and the life times of the excited states of the atom is presented. It is rigorously proven that these quantities are analytic functions of the momentum p of the atom and of the coupling constant λ0, provided | p| < mc and |ℑ p| and |λ0| are sufficiently small. The proof relies on a somewhat novel inductive construction involving a sequence of 'smooth Feshbach-Schur maps' applied to a complex dilatation of the original Hamiltonian, which yields an algorithm for the calculation of resonance energies that converges super-exponentially fast.