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雷达卡
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
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