Download or read book Invariant Integrals in Physics written by Genady P. Cherepanov and published by Springer Nature. This book was released on 2019-10-24 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, all physical laws are derived from a small number of invariant integrals which express the conservation of energy, mass, or momentum. This new approach allows us to unify the laws of theoretical physics, to simplify their derivation, and to discover some novel or more universal laws. Newton's Law of gravity is generalized to take into account cosmic forces of repulsion, Archimedes' principle of buoyancy is modified for account of the surface tension, and Coulomb's Laws for rolling friction and for the interaction of electric charges are substantially repaired and generalized. For postgraduate students, lecturers and researchers.

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 359 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.

Download or read book Path Integrals in Quantum Mechanics Statistics Polymer Physics and Financial Markets written by Hagen Kleinert and published by World Scientific Publishing Company. This book was released on 2004-03-05 with total page 1505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third, significantly 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. Request Inspection Copy

Download or read book Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets 5th Edition written by Hagen Kleinert and published by World Scientific. This book was released on 2009-05-18 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth, 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 been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes 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, coordinate-independent 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 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 results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena.Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order perturbation theory now also applies to small orders.Special attention is devoted to path integrals with topological restrictions needed to understand 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, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.

Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio Albeverio and published by Springer. This book was released on 2008-05-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

Download or read book Renormalization and Invariance in Quantum Field Theory written by Eduardo Caianiello and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter of this Advanced Study Institute, which has been rendered possible by the generous support of NATO, gratefully acknow ledged here, is of central importance to quantum field theory today. The problems involved are both deep and complicated, to a point that perhaps does not find easily a parallel in other branches of theoret ical physics. From the first rule-of-thumb prescriptions on how to perform renormalization to the most recent advances--which brighten our hopes to find, eventually, in field theory indications as to the ultimate composition of matter--a great amount of progress has cer tainly been made. We were fortunate to have among us many of the people who have most contributed to past and recent developments. Although clues that point to what to do next are clearer now than might have been expected only a few years ago, much hard work is still ahead. It is hoped that both our meeting, which brought to gether leaders in the field as well as bright and eager beginners, and the present volume, based on the NATO meeting, may be useful as a mise-a-point and as an up-to-date reference book for researchers interested in the field.

Download or read book Path Integrals in Quantum Mechanics Statistics Polymer Physics and Financial Markets written by Hagen Kleinert and published by World Scientific Publishing Company. This book was released on 2006 with total page 1602 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.

Download or read book Classical and Quantum Dynamics written by Walter Dittrich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here a detailed treatment many worked examples. This new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.

Download or read book Functional Integrals in Quantum Field Theory and Statistical Physics written by V.N. Popov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Path Integrals in Field Theory written by Ulrich Mosel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise textbook intended as a primer on path integral formalism both in classical and quantum field theories, although emphasis is on the latter. It is ideally suited as an intensive one-semester course, delivering the basics needed by readers to follow developments in field theory. Path Integrals in Field Theory paves the way for both more rigorous studies in fundamental mathematical issues as well as for applications in hadron, particle and nuclear physics, thus addressing students in mathematical and theoretical physics alike. Assuming some background in relativistic quantum theory (but none in field theory), it complements the authors monograph Fields, Symmetries, and Quarks (Springer, 1999).

Download or read book Path Integrals and Quantum Processes written by Mark S. Swanson and published by Courier Corporation. This book was released on 2014-02-19 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Equivariant Cohomology and Localization of Path Integrals written by Richard J. Szabo and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.

Download or read book Quantum Field Theory and Functional Integrals written by Nima Moshayedi and published by Springer Nature. This book was released on 2023-07-17 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Described here is Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view. Therein lies the main focus of Euclidean field theory. The notion of Gaussian measure and the construction of the Wiener measure are covered. As well, the notion of classical mechanics and the Schrödinger picture of quantum mechanics are recalled. There, the equivalence to the path integral formalism is shown by deriving the quantum mechanical propagator from it. Additionally, an introduction to elements of constructive quantum field theory is provided for readers.

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.

Download or read book Path Integrals and Coherent States of SU 2 and SU 1 1 written by Akira Inomata and published by World Scientific. This book was released on 1992 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent states, formulation of coherent path integrals for spin and unitary spin, and semiclassical quantization are presented. Applications are made to the study of quantum fluctuation, the nonlinear field model and phase holonomy.The final chapters present the theory of the SU(1, 1) coherent states and their applications. The radial coulomb problem, the Morse oscillator, and the large-N approximation are discussed. Applications to problems in quantum optics such as squeezed states, interaction with the squeezed vacuum states, and phase operator formalism are also included.This book will be useful as an introduction to the subject as well as a valuable work of reference.

Download or read book Volume and Surface Integrals Used in Physics written by J. G. Leathem and published by Cambridge University Press. This book was released on 2015-03-26 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1913, this book provides a concise account regarding volume and surface integrals used in physics.

Download or read book Path Integrals on Group Manifolds written by Wolfgang Tom‚ and published by World Scientific. This book was released on 1998 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author explains the theory clearly and the book is almost self-contained Contemporary Physics, 2000