Stochastic Mechanics

The Unification of Quantum Mechanics with Brownian Motion

Folkert Kuipers

$94.95 $81.12

Paperback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Springer International Publishing AG
01 June 2023

Probability & statistics; Stochastics; Quantum physics (quantum mechanics & quantum field theory); Statistical physics; Mathematical physics

Series: SpringerBriefs in Physics

Stochastic mechanics is a theory that holds great promise in resolving the mathematical and interpretational issues encountered in the canonical and path integral formulations of quantum theories. It provides an equivalent formulation of quantum theories, but substantiates it with a mathematically rigorous stochastic interpretation by means of a stochastic quantization prescription. 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.

By: Folkert Kuipers
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2023
Dimensions: Height: 235mm, Width: 155mm,
Weight: 221g
ISBN: 9783031314476
ISBN 10: 3031314476
Series: SpringerBriefs in Physics
Pages: 125
Publication Date: 01 June 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Dr. Folkert Kuipers is a postdoctoral researcher in quantum gravity at the Istituto Nazionale di Fisica Nucleare (INFN) in Naples, Italy. He holds B.Sc. degrees in Mathematics, Physics and Astronomy (Utrecht University, 2015), M.Sc. degrees in Theoretical Physics and Applied Mathematics (Utrecht University, 2018) and a Ph.D. degree in Theoretical and Mathematical Physics (University of Sussex, 2022). 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.

Reviews for Stochastic Mechanics: The Unification of Quantum Mechanics with Brownian Motion

“This is a textbook through which one can systematically comprehend the concepts of stochastic mechanics. Discussions pertaining to stochastic mechanics, developed both in the original period and in contemporary days, are introduced. Stochastic mechanics is a very interesting subject in mathematical physics, functional analysis, stochastic analysis and more … This textbook has a self-consistent style with an instructive appendix and replete references.” (Minoru Washizu Yoshida, Mathematical Reviews, October, 2024)