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Path Integral Quantization And Stochastic Quantization
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Book Synopsis Path Integral Quantization and Stochastic Quantization by : Michio Masujima
Download or read book Path Integral Quantization and Stochastic Quantization written by Michio Masujima and published by Springer Science & Business Media. This book was released on 2008-11-21 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Quantization by : Mikio Namiki
Download or read book Stochastic Quantization written by Mikio Namiki and published by Springer Science & Business Media. This book was released on 2008-10-04 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on stochastic quantization which was originally proposed by G. Parisi and Y. S. Wu in 1981 and then developed by many workers. I assume that the reader has finished a standard course in quantum field theory. The Parisi-Wu stochastic quantization method gives quantum mechanics as the thermal-equilibrium limit of a hypothetical stochastic process with respect to some fictitious time other than ordinary time. We can consider this to be a third method of quantization; remarkably different from the conventional theories, i. e, the canonical and path-integral ones. Over the past ten years, we have seen the technical merits of this method in quantizing gauge fields and in performing large numerical simulations, which have never been obtained by the other methods. I believe that the stochastic quantization method has the potential to extend the territory of quantum mechanics and of quantum field theory. However, I should remark that stochastic quantization is still under development through many mathematical improvements and physical applications, and also that the fictitious time of the theory is only a mathematical tool, for which we do not yet know its origin in the physical background. For these reasons, in this book, I attempt to describe its theoretical formulation in detail as well as practical achievements.
Book Synopsis Path Integral Methods in Quantum Field Theory by : R. J. Rivers
Download or read book Path Integral Methods in Quantum Field Theory written by R. J. Rivers and published by Cambridge University Press. This book was released on 1988-10-27 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Path Integrals in Physics by : M Chaichian
Download or read book Path Integrals in Physics written by M Chaichian and published by CRC Press. This book was released on 2019-08-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in 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. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.
Book Synopsis Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by : Hagen Kleinert
Download or read book Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets written by Hagen Kleinert and published by World Scientific. This book was released on 2009 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Path Integrals in Physics by : M Chaichian
Download or read book Path Integrals in Physics written by M Chaichian and published by CRC Press. This book was released on 2001-07-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Theory of Many-variable Systems and Fields by : B. Sakita
Download or read book Quantum Theory of Many-variable Systems and Fields written by B. Sakita and published by World Scientific Publishing Company. This book was released on 1985 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are based on special courses on Field Theory and Statistical Mechanics given for graduate students at the City College of New York. It is an ideal text for a one-semester course on Quantum Field Theory.
Book Synopsis Path Integrals in Quantum Mechanics by : Jean Zinn-Justin
Download or read book Path Integrals in Quantum Mechanics written by Jean Zinn-Justin and published by . This book was released on 2010-07-08 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Quantization by : Poul Henrik Damgaard
Download or read book Stochastic Quantization written by Poul Henrik Damgaard and published by World Scientific. This book was released on 1988 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of selected reprints presents as broad a selection as possible, emphasizing formal and numerical aspects of Stochastic Quantization. It reviews and explains the most important concepts placing selected reprints and crucial papers into perspective and compact form.
Book Synopsis Path Integrals in Physics by : M Chaichian
Download or read book Path Integrals in Physics written by M Chaichian and published by CRC Press. This book was released on 2018-10-08 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Realistic Interpretation of Quantum Mechanics by : Emilio Santos Corchero
Download or read book Realistic Interpretation of Quantum Mechanics written by Emilio Santos Corchero and published by Cambridge Scholars Publishing. This book was released on 2022-02-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Einstein “a physical theory should offer a picture of reality”. This made him frustrated and dissatisfied with the standard interpretation (or lack thereof) of quantum theory, since attempts to get a “picture” from it soon led to contradictions like the wave-particle duality. This book provides such a picture of the quantum world, that is, a “realistic interpretation”. Of course, this needs to be done in a way that is compatible with today’s experimental evidence, including the experiments that seem to contradict (local) realism. The book also offers a personal view on the meaning of general relativity and its relation with quantum mechanics, proposing a new perspective for dark energy, dark matter and stellar collapse. It is the result and a summary of the author’s extensive research on the foundations of quantum mechanics, spanning more than 50 years.
Book Synopsis Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes) by : Sultan Catto
Download or read book Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes) written by Sultan Catto and published by World Scientific. This book was released on 1992-01-27 with total page 1228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research.The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.
Book Synopsis Path Integrals and Hamiltonians by : Belal E. Baaquie
Download or read book Path Integrals and Hamiltonians written by Belal E. Baaquie and published by Cambridge University Press. This book was released on 2014-03-27 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.
Book Synopsis Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (4th Edition) by : Hagen Kleinert
Download or read book Path Integrals In Quantum Mechanics, Statistics, Polymer Physics, And Financial Markets (4th Edition) written by Hagen Kleinert and published by World Scientific Publishing Company. This book was released on 2006-07-19 with total page 1593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals.Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders.Special attention is devoted to path integrals with 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.The author's other book on ‘Critical Properties of φ4 Theories’ gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
Book Synopsis Sparse Grids and Applications - Munich 2012 by : Jochen Garcke
Download or read book Sparse Grids and Applications - Munich 2012 written by Jochen Garcke and published by Springer Science & Business Media. This book was released on 2014-04-11 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.
Book Synopsis Lectures on the Geometry of Quantization by : Sean Bates
Download or read book Lectures on the Geometry of Quantization written by Sean Bates and published by American Mathematical Soc.. This book was released on 1997 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.
Book Synopsis Path Integration: Trieste 1991, Lectures On - Proceedings Of The Adriatico Research Conference by : H A Cerdeira
Download or read book Path Integration: Trieste 1991, Lectures On - Proceedings Of The Adriatico Research Conference written by H A Cerdeira and published by World Scientific. This book was released on 1993-02-27 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of pedagogical lectures and research papers that were presented during a combined course/conference program held at the International Centre for Theoretical Physics in Trieste in the summer of 1991. The lectures begin from an elementary level and were intended to bring student participants to the point where they could appreciate the research conference that came at the end of program.
