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Functional Integration and Quantum Physics: Second Edition

Barry Simon California Institute of Technology, Pasadena, CA
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-0-8218-3582-1
Product Code: CHEL/351.H
List Price: $49.00 MAA Member Price:$44.10
AMS Member Price: $44.10 Electronic ISBN: 978-1-4704-3027-6 Product Code: CHEL/351.H.E List Price:$46.00
MAA Member Price: $41.40 AMS Member Price:$41.40
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List Price: $73.50 MAA Member Price:$66.15
AMS Member Price: $66.15 Click above image for expanded view Functional Integration and Quantum Physics: Second Edition Barry Simon California Institute of Technology, Pasadena, CA AMS Chelsea Publishing: An Imprint of the American Mathematical Society Available Formats:  Hardcover ISBN: 978-0-8218-3582-1 Product Code: CHEL/351.H  List Price:$49.00 MAA Member Price: $44.10 AMS Member Price:$44.10
 Electronic ISBN: 978-1-4704-3027-6 Product Code: CHEL/351.H.E
 List Price: $46.00 MAA Member Price:$41.40 AMS Member Price: $41.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$73.50 MAA Member Price: $66.15 AMS Member Price:$66.15
• Book Details

AMS Chelsea Publishing
Volume: 3512005; 306 pp
MSC: Primary 81; Secondary 58; 60;

The main theme of this book is the “path integral technique” and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of the Feynman–Kac formula. Starting with the main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the Feynman–Kac formula. Also included is a simple exposition of stochastic Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman–Kac–Itô formula).

Among other topics discussed are the probabilistic approach to the bound of the number of ground states of correlation inequalities (the Birman–Schwinger principle, Lieb's formula, etc.), the calculation of asymptotics for functional integrals of Laplace type (the theory of Donsker–Varadhan) and applications, scattering theory, the theory of crushed ice, and the Wiener sausage.

Written with great care and containing many highly illuminating examples, this classic book is highly recommended to anyone interested in applications of functional integration to quantum physics. It can also serve as a textbook for a course in functional integration.

Graduate students and research mathematicians interested in probability and applications of functional integration to quantum physics.

• Chapters
• Introduction
• The basic processes
• Bound state problems
• Inequalities
• Magnetic fields and stochastic integrals
• Asymptotics
• Other topics
• References
• Request Review Copy
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Volume: 3512005; 306 pp
MSC: Primary 81; Secondary 58; 60;

The main theme of this book is the “path integral technique” and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of the Feynman–Kac formula. Starting with the main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the Feynman–Kac formula. Also included is a simple exposition of stochastic Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman–Kac–Itô formula).

Among other topics discussed are the probabilistic approach to the bound of the number of ground states of correlation inequalities (the Birman–Schwinger principle, Lieb's formula, etc.), the calculation of asymptotics for functional integrals of Laplace type (the theory of Donsker–Varadhan) and applications, scattering theory, the theory of crushed ice, and the Wiener sausage.

Written with great care and containing many highly illuminating examples, this classic book is highly recommended to anyone interested in applications of functional integration to quantum physics. It can also serve as a textbook for a course in functional integration.