Functional Integrals And Statistical Physics
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| Author | : V.N. Popov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 316 |
| Release | : 2001-11-30 |
| Genre | : Science |
| ISBN | : 9781402003073 |
Functional integration is one of the most powerful methods of contempo rary theoretical physics, enabling us to simplify, accelerate, and make clearer the process of the theoretician's analytical work. Interest in this method and the endeavour to master it creatively grows incessantly. This book presents a study of the application of functional integration methods to a wide range of contemporary theoretical physics problems. The concept of a functional integral is introduced as a method of quantizing finite-dimensional mechanical systems, as an alternative to ordinary quantum mechanics. The problems of systems quantization with constraints and the manifolds quantization are presented here for the first time in a monograph. The application of the functional integration methods to systems with an infinite number of degrees of freedom allows one to uniquely introduce and formulate the diagram perturbation theory in quantum field theory and statistical physics. This approach is significantly simpler than the widely accepted method using an operator approach.
| Author | : Lukong Cornelius Fai |
| Publisher | : CRC Press |
| Total Pages | : 394 |
| Release | : 2021-04-16 |
| Genre | : Science |
| ISBN | : 1000349063 |
This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.
| Author | : Hagen Kleinert |
| Publisher | : World Scientific |
| Total Pages | : 1626 |
| Release | : 2009 |
| Genre | : Business & Economics |
| ISBN | : 9814273570 |
Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.
| Author | : Victor Nikolaevich Popov |
| Publisher | : Cambridge University Press |
| Total Pages | : 240 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 9780521407878 |
This book describes the theory and selected applications of one of the most important mathematical tools used in the theoretical investigation of collective excitations in statistical physics, such as occur in superfluidity, superconductivity, plasma dynamics, superradiation, and in phase transitions.
| Author | : M Chaichian |
| Publisher | : CRC Press |
| Total Pages | : 368 |
| Release | : 2001-07-01 |
| Genre | : Science |
| ISBN | : 9780750308021 |
The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
| Author | : A.D. Egorov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 421 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401117616 |
Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes. This monograph is devoted to numerical approximation methods of continual integration. A systematic description is given of the approximate computation methods of functional integrals on a wide class of measures, including measures generated by homogeneous random processes with independent increments and Gaussian processes. Many applications to problems which originate from analysis, probability and quantum physics are presented. This book will be of interest to mathematicians and physicists, including specialists in computational mathematics, functional and statistical physics, nuclear physics and quantum optics.
| Author | : S. G. Brush |
| Publisher | : |
| Total Pages | : 42 |
| Release | : 1959 |
| Genre | : |
| ISBN | : |
| Author | : Kerson Huang |
| Publisher | : John Wiley & Sons |
| Total Pages | : 446 |
| Release | : 2008-09-26 |
| Genre | : Science |
| ISBN | : 3527617388 |
A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained. Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features: * Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization * A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations * Nineteen self-contained chapters with exercises, supplemented with graphs and charts
| Author | : James Glimm |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 551 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461247284 |
Describes fifteen years' work which has led to the construc- tion of solutions to non-linear relativistic local field e- quations in 2 and 3 space-time dimensions. Gives proof of the existence theorem in 2 dimensions and describes many properties of the solutions.
| Author | : Barry Simon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 322 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821835823 |
Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.
