• 1 / Quantum Kinematics of Unstable Systems.- 1.1. Is There Anything Left to Study on Unstable Systems?.- 1.2. Basic Notions.- 1.3. Small-Time Behaviour.- 1.4. The Inverse Decay Problem.- 1.5. Semiboundedness and Other Properties of the Energy Spectrum.- 1.6. Bounded-Energy Approximation.- Notes to Chapter 1.- 2 / Repeated Measurements on Unstable Systems.- 2.1. Decay Law in the Presence of Repeated Measurements.- 2.2. Periodically Structured Measuring Devices.- 2.3. A Model: Charged Kaons in a Bubble Chamber.- 2.4. Limit of Continual Observation and the ‘Zeno’s Paradox’.- Notes to Chapter 2.- 3 / Dynamics and Symmetries.- 3.1. Poles of the Reduced Resolvent.- 3.2. Friedrichs Model.- 3.3. Bounded Perturbations of Embedded Eigenvalues.- 3.4. Symmetries and Broken Symmetries.- 4 / Pseudo-Hamiltonians.- 4.1. Pseudo-Hamiltonians and Quasi-Hamiltonians.- 4.2. Maximal Dissipative Operators.- 4.3. Schrödinger Pseudo-Hamiltonians.- 4.4. The Optical Approximation.- 4.5. Non-unitary Scattering Theory.- Notes to Chapter 4.- 5 / Feynman Path Integrals.- 5.1. The Integrals that are not Integrals: a Brief Survey.- 5.2. Feynman Maps on the Algebra ?(?).- 5.3. Hilbert Spaces of Paths.- 5.4. Polygonal-Path Approximations.- 5.5. Product Formulae.- 5.6. More about Other F-Integral Theories.- Notes to Chapter 5.- 6 / Application to Schrödinger Pseudo-Hamiltonians.- 6.1. Feynman—Cameron—Itô Formu la.- 6.2. The Damped Harmonic Oscillator.- 6.3. The ‘Feynman Paths’.- Notes to Chapter 6.- Selected Problems.

'The careful and comprehensive treatment given in the book, utilizing a wide range of modern analysis (...) is accompanied by equally careful discussion of the physics involved, so that it should be accessible and useful to a wide range of mathematicians, physicists, to whom it is primarily directed.' Mathematical Reviews (1986) '...the best and most comprehensive exposition that has appeared so far. ... ...I am tremendously impressed by individuals who have mastered large parts of both the physics of modern quantum theory and the associated rigorous mathematics; Exner is one of these individuals. I heartily recommend his book.' Foundations of Physics, 15 (1985)