Overview
- Gives a new perspective on many open problems in quantum foundations
- Presents a unique outlook on stochastic geometry and quantum gravity
- Provides a review of modern stochastic mechanics
Part of the book series: SpringerBriefs in Physics (SpringerBriefs in Physics)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
- Quantum Mechanics
- Quantum Foundations
- Quantum Axioms
- Unitary Diffusion
- Quantum Foam
- Spacetime Symmetries
- Second Order Geometry
- Ito Group
- Stochastic Process
- Quadratic Variation
- Stochastic Mechanics
- Brownian Motion
- Diffusion Theory
- Stochastic Quantization
- Stochastic Interpretation
- Stochastic Geometry
- Wiener Process
- Stochastic Calculus
- Structure Relation
About this book
The book builds on recent developments in this theory, and shows that quantum mechanics can be unified with the theory of Brownian motion in a single mathematical framework. Moreover, it discusses the extension of the theory to curved spacetime using second order geometry, and the induced Itô deformations of the spacetime symmetries.
The book is self-contained and provides an extensive review of stochastic mechanics of the single spinless particle. The book builds up the theory on a step by step basis. It starts, in chapter 2, with a review of the classical particle subjected to scalar and vector potentials. In chapter 3, the theory is extended to the study of a Brownian motion in any potential, by the introduction of a Gaussian noise. In chapter 4, the Gaussian noise is complexified. The result is a complex diffusion theory that contains both Brownian motion and quantum mechanics as a special limit. In chapters 5, the theory is extended to relativistic diffusion theories. In chapter 6, the theory is further generalized to the context of pseudo-Riemannian geometry. Finally, in chapter 7, some interpretational aspects of the stochastic theory are discussed in more detail. The appendices concisely review relevant notions from probability theory, stochastic processes, stochastic calculus, stochastic differential geometry and stochastic variational calculus.
The book is aimed at graduate students and researchers in theoretical physics and applied mathematics with an interest in the foundations of quantum theory andBrownian motion. The book can be used as reference material for courses on and further research in stochastic mechanics, stochastic quantization, diffusion theories on curved spacetimes and quantum gravity.
Authors and Affiliations
About the author
His research interests range over many aspects of quantum theories on curved spacetimes and quantum gravity. Within these fields, he has contributed to research on effective field theories of quantum gravity. In addition, he made various important contributions to the study of stochastic mechanics and its extensions to curved spacetimes using second order geometry.
For his proposal to apply stochastic differential geometry to the study of quantum gravity, he has been awarded a Humboldt fellowship, which will be carried out at the LMU in Munich.
Bibliographic Information
Book Title: Stochastic Mechanics
Book Subtitle: The Unification of Quantum Mechanics with Brownian Motion
Authors: Folkert Kuipers
Series Title: SpringerBriefs in Physics
DOI: https://doi.org/10.1007/978-3-031-31448-3
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Softcover ISBN: 978-3-031-31447-6Published: 01 June 2023
eBook ISBN: 978-3-031-31448-3Published: 31 May 2023
Series ISSN: 2191-5423
Series E-ISSN: 2191-5431
Edition Number: 1
Number of Pages: IX, 125
Number of Illustrations: 1 b/w illustrations
Topics: Quantum Physics, Probability Theory and Stochastic Processes, Theoretical, Mathematical and Computational Physics, Mathematical Methods in Physics