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Author: Akira Inomata Publisher: World Scientific ISBN: 9789810206567 Category : Science Languages : en Pages : 338
Book Description
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.
Author: Akira Inomata Publisher: World Scientific ISBN: 9789810206567 Category : Science Languages : en Pages : 338
Book Description
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.
Author: Wolfgang Tomé Publisher: World Scientific ISBN: 9814496553 Category : Science Languages : en Pages : 232
Book Description
The quantization of physical systems moving on group and symmetric spaces has been an area of active research over the past three decades. This book shows that it is possible to introduce a representation-independent propagator for a real, separable, connected and simply connected Lie group with irreducible, square-integrable representations. For a given set of kinematical variables this propagator is a single generalized function independent of any particular choice of fiducial vector and the irreducible representations of the Lie group generated by these kinematical variables, which nonetheless correctly propagates each element of a continuous representation based on the coherent states associated with these kinematical variables. Furthermore, the book shows that it is possible to construct regularized lattice phase space path integrals for a real, separable, connected and simply connected Lie group with irreducible, square-integrable representations, and although the configuration space is in general a multidimensional curved manifold, it is shown that the resulting lattice phase space path integral has the form of a lattice phase space path integral on a multidimensional flat manifold. Hence, a novel and extremely natural phase space path integral quantization is obtained for general physical systems whose kinematical variables are the generators of a connected and simply connected Lie group. This novel phase space path integral quantization is (a) exact, (b) more general than, and (c) free from the limitations of the previously considered path integral quantizations of free physical systems moving on group manifolds. To illustrate the general theory, a representation-independent propagator is explicitly constructed for SU(2) and the affine group. Contents:Mathematical PreludePhysical PreludeA Review of Some Means to Define Path Integrals on Group and Symmetric SpacesNotations and PreliminariesThe Representation Independent Propagator for a General Lie GroupClassical Limit of the Representation Independent PropagatorConclusion and OutlookContinuous Representation TheoryExact Lattice Calculations Readership: Physicists. Keywords:Global Analysis;Analysis on Manifolds [For Geometric Integration Theory];Spaces and Manifolds of Mappings;Quantum Mechanics (Feynman Path Integrals), Relativity, Fluid Dynamics;Quantum Theory;General Quantum Mechanics and Problems of Quantization;Path IntegralsReviews: “The author explains the theory clearly and the book is almost self-contained …” Contemporary Physics
Author: John R. Klauder Publisher: Springer Science & Business Media ISBN: 0817647910 Category : Mathematics Languages : en Pages : 292
Book Description
This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Author: Mark S. Swanson Publisher: Academic Press ISBN: Category : Mathematics Languages : en Pages : 464
Book Description
In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-study.
Author: Theodore T. Allen Publisher: Springer Science & Business Media ISBN: 1849960003 Category : Technology & Engineering Languages : en Pages : 572
Book Description
Lean production, has long been regarded as critical to business success in many industries. Over the last ten years, instruction in six sigma has been increasingly linked with learning about the elements of lean production. Introduction to Engineering Statistics and Lean Sigma builds on the success of its first edition (Introduction to Engineering Statistics and Six Sigma) to reflect the growing importance of the "lean sigma" hybrid. As well as providing detailed definitions and case studies of all six sigma methods, Introduction to Engineering Statistics and Lean Sigma forms one of few sources on the relationship between operations research techniques and lean sigma. Readers will be given the information necessary to determine which sigma methods to apply in which situation, and to predict why and when a particular method may not be effective. Methods covered include: • control charts and advanced control charts, • failure mode and effects analysis, • Taguchi methods, • gauge R&R, and • genetic algorithms. The second edition also greatly expands the discussion of Design For Six Sigma (DFSS), which is critical for many organizations that seek to deliver desirable products that work first time. It incorporates recently emerging formulations of DFSS from industry leaders and offers more introductory material on the design of experiments, and on two level and full factorial experiments, to help improve student intuition-building and retention. The emphasis on lean production, combined with recent methods relating to Design for Six Sigma (DFSS), makes Introduction to Engineering Statistics and Lean Sigma a practical, up-to-date resource for advanced students, educators, and practitioners.
Author: J. Leite Lopes Publisher: Elsevier ISBN: 1483278972 Category : Science Languages : en Pages : 500
Book Description
Gauge Field Theories: An Introduction covers the basic notions and principles of gauge theories. This book is composed of 10 chapters that focus on the Salam-Weinberg model of electro-weak interactions of neutrino-lepton scattering, as well as the Parton model. The first chapter is an introduction to solitons and instantons, as well as the topological quantum numbers, subjects that arose from the study of the non-linear field equations in gauge theories. The succeeding chapters deal with the concept of gravitational field, electrodynamical systems, the Yang-mills gauge fields, and the Higgs mechanism. The remaining chapters highlight the speculations on possible lepton and quark structured. These chapters present the SU(5) model of grand unification. This book will prove useful to physics university and advanced high school students.
Author: Akira Inomata
Author: Akira Inomata
Author: Wolfgang Tomé
Author: John R. Klauder
Author: Wolfgang Tom
Author: Mark S. Swanson
Author: Theodore T. Allen
Author: J. Leite Lopes
Author: 
Author: 
Author: Abdyrakhman G. Gubaev