From the book reviews:
“This monograph represents a nice survey written in a concise and lucid manner, enabling the reader to quickly and easily grasp the main aspects and ideas of quantum stochastic processes. … The book is suitable for graduate students or researchers who work in the field of mathematics and physics.” (Dora Seleši, Mathematical Reviews, February, 2015)
A Measure Theoretical Approach to Quantum Stochastic Processes
von Wilhelm WaldenfelsThis monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as power series of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory.
Considering in detail four basic examples (e. g. a two-level atom coupled to a heat bath of oscillators), in each case the Hamiltonian of the associated one-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors.
Advanced topics include the theory of the Hudson-Parthasarathy equation and the amplified oscillator problem. To that end, a chapter on white noise calculus has also been included.
