Stochastic Processes in Quantum Physics

✍ Scribed by Masao Nagasawa (auth.)

• Publisher: Birkhäuser Basel
• Year: 2000
• Tongue: English
• Leaves: 608
• Series: Monographs in Mathematics 94
• Edition: 1
• Category: Library

✦ Synopsis

"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

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

✦ Subjects

Quantum Physics;Probability Theory and Stochastic Processes