Stochastic Processes in Quantum Physics

Authors: Masao Nagasawa



"Stochastic Processes in Quantum Physics" addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous. Together with known techniques, some new stochastic methods are applied in solving the equation of motion and the equation of dynamics of relativistic quantum particles. The problem of the origin of universes is discussed as an application of the theory. The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level, and some selected chapters can be used as (sub-)textbooks for advanced courses on stochastic processes, quantum theory and theoretical chemistry.

Table of contents (16 chapters)

Front Matter
Pages N3-VII

Markov Processes
Pages 1-26

Time Reversal and Duality
Pages 27-52

Non-Relativistic Quantum Theory
Pages 53-104

Stationary Schrödinger Processes
Pages 105-137

Construction of the Schrödinger Processes
Pages 139-184

Markov Processes with Jumps
Pages 185-229

Relativistic Quantum Particles
Pages 231-262

Stochastic Differential Equations of Pure-Jumps
Pages 263-285

Variational Principle for Relativistic Quantum Particles
Pages 287-313

Time Dependent Subordination and Markov Processes with Jumps
Pages 315-354


Concave Majorants of Lévy Processes and the Light Cone
Pages 355-388

The Locality in Quantum Physics
Pages 389-435

Micro Statistical Theory
Pages 437-460

Processes on Open Time Intervals
Pages 461-500

Creation and Killing of Particles
Pages 501-519

The Itô Calculus
Pages 521-571

Back Matter
Pages 573-598