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Author: Mark S Swanson
Publisher:
ISBN: 9780750335485
Category :
Languages : en
Pages : 242
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Book Description
This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. Self-contained guide for students and practitioners
Author: Mark S Swanson
Publisher:
ISBN: 9780750335485
Category :
Languages : en
Pages : 242
Get Book Here
Book Description
This book is a self-contained and concise introduction to the techniques and applications of path integral quantization and functional techniques, aimed at students and practitioners. The first half of the text focuses on quantum mechanics, including a review of the action formulation of classical mechanics and quantum mechanics in the Dirac operator and state formalism, and further examination of the path integral. The second part examines relativistic field theories, reviewing special relativity, as well as derivation of the path integral representation of the vacuum transition element for quantized scalar, spinor, and vector fields from the coherent state representation of the respective field theories. Key Features Concise introduction to the derivation and methods of path integral approaches to quantum mechanics and quantum field theory. Self-contained guide for students and practitioners
Author: Michio Masujima
Publisher: Springer Science & Business Media
ISBN: 3540878513
Category : Science
Languages : en
Pages : 286
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Book Description
In this book, we discuss the path integral quantization and the stochastic quantization of classical mechanics and classical field theory. Forthe description ofthe classical theory, we have two methods, one based on the Lagrangian formalism and the other based on the Hamiltonian formal ism. The Hamiltonian formalism is derived from the Lagrangian·formalism. In the standard formalism ofquantum mechanics, we usually make use ofthe Hamiltonian formalism. This fact originates from the following circumstance which dates back to the birth of quantum mechanics. The first formalism ofquantum mechanics is Schrodinger's wave mechan ics. In this approach, we regard the Hamilton-Jacobi equation of analytical mechanics as the Eikonal equation of "geometrical mechanics". Based on the optical analogy, we obtain the Schrodinger equation as a result ofthe inverse of the Eikonal approximation to the Hamilton-Jacobi equation, and thus we arrive at "wave mechanics". The second formalism ofquantum mechanics is Heisenberg's "matrix me chanics". In this approach, we arrive at the Heisenberg equation of motion from consideration of the consistency of the Ritz combination principle, the Bohr quantization condition and the Fourier analysis of a physical quantity. These two formalisms make up the Hamiltonian.formalism of quantum me chanics.
Author: Herbert W. Hamber
Publisher: Springer Science & Business Media
ISBN: 354085293X
Category : Science
Languages : en
Pages : 342
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Book Description
"Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.
Author: Mark S. Swanson
Publisher: Courier Corporation
ISBN: 0486493067
Category : Science
Languages : en
Pages : 463
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Book Description
Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.
Author: R. J. Rivers
Publisher: Cambridge University Press
ISBN: 9780521368704
Category : Science
Languages : en
Pages : 356
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Book Description
The applications of functional integral methods introduced in this text for solving a range of problems in quantum field theory will prove useful for students and researchers in theoretical physics and quantum field theory.
Author: Heinz J Rothe
Publisher: World Scientific
ISBN: 9814602302
Category :
Languages : en
Pages : 397
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Book Description
This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.
Author: Hagen Kleinert
Publisher: World Scientific
ISBN: 9814273570
Category : Business & Economics
Languages : en
Pages : 1626
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Book Description
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: Gert Roepstorff
Publisher: Springer Science & Business Media
ISBN: 3642578861
Category : Science
Languages : en
Pages : 400
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Book Description
Specifically designed to introduce graduate students to the functional integration method in contemporary physics as painlessly as possible, the book concentrates on the conceptual problems inherent in the path integral formalism. Throughout, the striking interplay between stochastic processes, statistical physics and quantum mechanics comes to the fore, and all the methods of fundamental interest are generously illustrated by important physical examples.
Author: Jean Zinn-Justin
Publisher:
ISBN: 0198566751
Category : Mathematics
Languages : en
Pages : 336
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Book Description
Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.
Author: M Chaichian
Publisher: CRC Press
ISBN: 9780750308021
Category : Science
Languages : en
Pages : 368
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Book Description
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.
