Hardcover ISBN:  9780821835821 
Product Code:  CHEL/351.H 
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Electronic ISBN:  9781470430276 
Product Code:  CHEL/351.H.E 
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Book DetailsAMS Chelsea PublishingVolume: 351; 2005; 306 ppMSC: 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.ReadershipGraduate students and research mathematicians interested in probability and applications of functional integration to quantum physics.

Table of Contents

Chapters

Introduction

The basic processes

Bound state problems

Inequalities

Magnetic fields and stochastic integrals

Asymptotics

Other topics

References


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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