Path Integrals And Coherent States Of Su 2 And Su 1 1
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Path Integrals and Coherent States of SU(2) and SU(1,1) by Akira Inomata,Hiroshi Kuratsuji,Christopher C. Gerry Pdf
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.
Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference by Valerio Tognetti,Roberto Casalbuoni,Riccardo Giachetti,Ruggero Vaia,Paola Verrucchi Pdf
This book contains the invited contributions to the 6th International Conference on Path Integrals from peV to TeV, held in Florence in 1998. The conference, devoted to functional integration, brought together many physicists with interests ranging from elementary particles to nuclear, solid state, liquid state, polymer and complex systems physics. The variety of topics is reflected in the book, which is a unique collection of papers on manifold applications of functional methods in several areas of physics.
On Klauder's Path: A Field Trip by G G Emch,G C Hegerfeldt,L Streit Pdf
This volume contains contributions by friends, colleagues and associates of John R Klauder on the occasion of his 60th birthday. Klauder's scientific work embraces vast territories from quantum theories to general relativity, optics and chaotic dynamics. A recurrent theme in his research is the role played by coherent states, in particular, in connection with path integral formulations of quantization. Perhaps at a less lofty level, this concept has had at least two spectacular applications: as a powerful investigative tool in quantum optics and as a precursor to wavelets. In a different vein, Klauder also attacked specific, non-renormalizable but exactly soluble, hard-core models in field theory, where he uncovered what has since been called the Klauder phenomenon. The contributors to this volume represent the special brand of mathematicians and physicists John Klauder helped define throughout his seminal career in the industrial and academic worlds. Contents:Preface (J R Klauder)A Remark on a Connection of Return to Equilibrium and Multiple Ground States in Some Perturbed XY–Model (H Araki)Covariance Sub-Algebras Connected with Symmetry Groups of C∗öAlgebras (H J Borchers)Coherent-State Path-Integrals and Their Relations to Wavelets (B De Facio)Brownian Motion and Its Conditional Descendants (P Garbaczweski)Path Integrals and Network Quantum Numbers (R Gilmore and M Jeffery)Reckoning of the Besselian Path Integral (A Inomata)On Q-Analogs of Coherent States (M A Lohe & L C Biedenharn)Coherent States and Squeezed States, Supercoherent States and Supersqueezed States (M M Nieto)How to Generate Thermal Photons — On the Computer (M R Schroeder)A Local Quantum Theory Without Positive Energy Representations (R F Streater)Quantum Noise and Thermal Noise (H Umezawa)and other papers Readership: Physicists and mathematicians. keywords:
Path Integrals in Physics by M Chaichian,A Demichev Pdf
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.
Mathematical Methods For Physicists by Danilo Babusci,Giuseppe Dattoli,Silvia Licciardi,Elio Sabia Pdf
The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide class of apparently disparate physical phenomena. An important role, within this respect, is provided by a nonconventional formulation of special functions and polynomials. The proposed methods simplify the understanding of the relevant technicalities and yield a unifying view to their applications in Physics as well as other branches of science.The chapters are not organized through the mathematical study of specific problems in Physics, rather they are suggested by the formalism itself. For example, it is shown how the matrix formalism is useful to treat ray Optics, atomic systems evolution, QED, QCD and Feynman diagrams. The methods presented here are simple but rigorous. They allow a fairly substantive tool of analysis for a variety of topics and are useful for beginners as well as the more experienced researchers.
This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals ? New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23?28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose?Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.
Equivariant Cohomology and Localization of Path Integrals by Richard J. Szabo Pdf
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.
Path Integrals, Hyperbolic Spaces and Selberg Trace Formulae by Christian Grosche Pdf
In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition. The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula. Contents:IntroductionPath Integrals in Quantum MechanicsSeparable Coordinate Systems on Spaces of Constant CurvaturePath Integrals in Pseudo-Euclidean GeometryPath Integrals in Euclidean SpacesPath Integrals on SpheresPath Integrals on HyperboloidsPath Integral on the Complex SpherePath Integrals on Hermitian Hyperbolic SpacePath Integrals on Darboux SpacesPath Integrals on Single-Sheeted HyperboloidsMiscellaneous Results on Path IntegrationBilliard Systems and Periodic Orbit TheoryThe Selberg Trace FormulaThe Selberg Super-Trace FormulaSummary and Discussion Readership: Graduate and researchers in mathematical physics. Keywords:Path Integrals;Selberg Trace Formula;Quantum Chaos;Coordinate Systems;Homogeneous Spaces;Spaces of Non-Constant Curvature;Separation of VariablesKey Features:The 2nd edition brings the text up to date with new developments and results in the fieldContains enumeration of many explicit path integrals solutionsReviews: “This book is a good survey of results in a fascinating, highly geometrical, field in which much remains to be done.” Zentralblatt MATH
Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulae by Christian Grosche Pdf
In this volume, a comprehensive review is given for path integration in two- and three-dimensional homogeneous spaces of constant curvature, including an enumeration of all coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, and their use in mathematical physics and quantum chaos. The volume also contains results on the study of the properties of a particular integrable billiard system in the hyperbolic plane, a proposal concerning interbasis expansions for spheroidal coordinate systems in four-dimensional Euclidean space, and some further results derived from the Selberg (super-) trace formula.
Coherent States by D H Feng,J R Klauder,M R Strayer Pdf
The book consists of lectures delivered at the International Symposium on Coherent States: Past, Present, and Future, held in Oak Ridge, Tennessee, June 14 – 17 1993. Both theoretical and experimental subjects are treated. Theoretical subjects dealt with include quantum optics, quantum chaos, condensed matter physics, nuclear physics, high energy physics and foundational issues such as quantum-classical connections and various semiclassical quantization schemes. Experimental topics dealt with principally concern atomic and molecular physics and especially lasers. Topics related to coherent states, most notably wavelets, are also included. Contents: Quantum Versus Classical Phase in Optical Systems (G S Agarwal)Coherent States: How Far Can One Go? (J-P Antoine)Orthonormal Bases of Coherent States: The Canonical Case and the axGroup (I Daubechies)Dynamics of Coherent States as the Diffusion Process: Schrödinger's System, Bernstein Processes, and Quantum Evolution (P Garbaczewski)Some Reflections on Coherence and Ion Trapping (R J Glauber)Coherent States, Chaos, and Information (E J Heller & S Tomsovic)Coherent States as a Tool for Obtaining Rigorous Bounds (E H Lieb)Classical-Quantum Correspondence in Time-Dependent Perturbation Theory (S M McRae & E R Vrscay)Asymptotic Coherence of Gluons and of q-Bosons (C A Nelson)Electron Nuclear Dynamics with Coherent States (Y Öhrn & E Deumens)Quantum Coherent Operators (J P Solovej)Classicalization and Coherent States (W-M Zhang & D H Feng)Post-Banquet Talk (A S Wightman)and other papers Readership: Theoretical and applied physicists and mathematicians.
Theory of Nonclassical States of Light by V.V. Dodonov,V.I. Man'ko Pdf
The term 'nonclassical states' refers to the quantum states that cannot be produced in the usual sources of light, such as lasers or lamps, rather than those requiring more sophisticated apparatus for their production. Theory of Non-classical States of Light describes the current status of the theory of nonclassical states of light including many new and important results as well as introductory material and the history of the subject. The authors concentrate on the most important types of nonclassical states, namely squeezed, even/odd ('Schrodinger cat') and binomial states, including their generalizations. However, a review of other types of nonclassical is also given in the introduction, and methods for generating nonclassical states on various processes of light-matter interaction, their phase-space description, and the time evolution of nonclassical states in these processes is presented in separate chapters. This contributed volume contains all of the necessary formulae and references required to gain a good understanding of the principles and current status of the field. It will provide a valuable information resource for advanced students and researchers in quantum physics.
Classical And Quantum Systems: Foundations And Symmetries - Proceedings Of The 2nd International Wigner Symposium by Heinz-dietrich Doebner,F Schroeck Jr,W Scherer Pdf
The Wigner Symposium series is focussed on fundamental problems and new developments in physics and their experimental, theoretical and mathematical aspects. Particular emphasis is given to those topics which have developed from the work of Eugene P Wigner. The 2nd Wigner symposium is centered around notions of symmetry and geometry, the foundations of quantum mechanics, quantum optics and particle physics. Other fields like dynamical systems, neural networks and physics of information are also represented.This volume brings together 19 plenary lectures which survey latest developments and more than 130 contributed research reports.
On Klauder's Path by Grard G. Emch,G. C. Hegerfeldt,Ludwig Streit Pdf
This volume contains contributions by friends, colleagues and associates of John R Klauder on the occasion of his 60th birthday.Klauder's scientific work embraces vast territories from quantum theories to general relativity, optics and chaotic dynamics. A recurrent theme in his research is the role played by coherent states, in particular, in connection with path integral formulations of quantization. Perhaps at a less lofty level, this concept has had at least two spectacular applications: as a powerful investigative tool in quantum optics and as a precursor to wavelets. In a different vein, Klauder also attacked specific, non-renormalizable but exactly soluble, hard-core models in field theory, where he uncovered what has since been called the Klauder phenomenon.The contributors to this volume represent the special brand of mathematicians and physicists John Klauder helped define throughout his seminal career in the industrial and academic worlds.
Coherent States, Wavelets, and Their Generalizations by Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Gazeau Pdf
This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research literature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.
Quantum Field Theory and Its Macroscopic Manifestations by Massimo Blasone,Petr Jizba,Giuseppe Vitiello Pdf
Quantum dynamics underlies macroscopic systems exhibiting some kind of ordering, such as superconductors, ferromagnets and crystals. Even large scale structures in the Universe and ordering in biological systems appear to be the manifestation of microscopic dynamics ruling their elementary components. The scope of this book is to answer questions such as: how it happens that the mesoscopic/macroscopic scale and stability characterizing those systems are dynamically generated out of the microscopic scale of fluctuating quantum components; how quantum particles coexist and interact with classically behaving macroscopic objects, e.g. vortices, magnetic domains and other topological defects. The quantum origin of topological defects and their interaction with quanta is a crucial issue for the understanding of symmetry breaking phase transitions and structure formation in a wide range of systems from condensed matter to cosmology. Deliberately not discussing other important problems, primarily renormalization problems, this book provides answers to such questions in a unitary, self-consistent physical and mathematical framework, which makes it unique in the panorama of existing texts on a similar subject. Crystals, ferromagnets and superconductors appear to be macroscopic quantum systems, i.e. their macroscopic properties cannot be explained without recourse to the underlying quantum dynamics. Recognizing that quantum field dynamics is not confined to the microscopic world is one of the achievements of this book, also marking its difference from other texts. The combined use of algebraic methods, and operator and functional formalism constitutes another distinctive, valuable feature. Contents:The Structure of the Space of the Physical StatesInequivalent Representations of the Canonical Commutation RelationsSpontaneous Breakdown of Symmetry and the Goldstone TheoremDynamical Rearrangement of Symmetry and Macroscopic Manifestations of QFTThermal Field Theory and Trajectories in the Space of the RepresentationsSelected Topics in Thermal Field TheoryTopological Defects as Non-Homogeneous Condensates. ITopological Defects as Non-Homogeneous Condensates. IIDissipation and QuantizationElements of Soliton Theory and Related Concepts Readership: Researchers in mathematical physics, theoretical physics, high energy physics, condensed matter physics and solid state physics. Advanced undergraduate and graduate students in physics. Keywords:Quantum Field Theory;Symmetry Breaking;Boson Condensation;Ordered Patterns;Coherent States;Phase Transitions;Topological Defects;Solitons;Vortices;Monopoles;Gauge Theories;Group Contraction;q-Groups;Hopf Algebra;Quantum DissipationKey Features:One of the achievements of this book, which marks its difference from other similar texts, is that quantum field dynamics is recognized to be not confined to the microscopic world. The combined use of algebraic methods, operator and functional formalism constitutes another distinctive valuable feature of this bookA wide range of physical systems are discussed in a unitary, self-consistent physical and mathematical frameworkThe systems considered range from condensed matter to cosmology, from fractals, neutrino oscillations to brain modelingReviews:“Physicists believe quantum fields to be the true protagonists of Nature in the full variety of its wonderful, manifold manifestations: from the fascinating appearance of colorful disclinations in nematic liquid crystals, to the awing pattern of cosmic strings in the Universe; from the unexpected quantum features of macroscopic superfluids, to the surprising dynamics of solitons, to the mysterious process of generation of virtual particles when symmetry after symmetry is broken. Quantum field theory is the tool they created to fulfill their visionary dream of describing with a universal, unique language all of nature, be it single particles or condensed matter, fields or many-body objects, in a way that can be made consistent with the other hard and deep constraint they have to call to account: relativistic covariance. This is perhaps the first book on quantum field theory whose aim is to grasp and describe with rigor and completeness, but at the same time in a compelling, fascinating way, all the facets of the complex challenge it faces scientists with. It is a book that presents solutions but poses questions as well; hard, demanding yet fascinating; a book that can at the same time be used as a textbook and as a book of dreams that any scientist would like to make come true.”Mario Rasetti Politecnico di Torino, Italy “This remarkable book dispels the common misconception that quantum field theory is 'just quantum mechanics with an infinite number of degrees of freedom', revealing vast new mathematical terrains, and new ways of understanding physical phenomena in both commonplace and exotic systems. Uniquely valuable, and covering material difficult or impossible to find coherently assembled elsewhere, it will be welcomed by students and researchers in all fields of physics and mathematics.”John Swain Northeastern University, USA “The book by Massimo Blasone, Petr Jizba and Giuseppe Vitiello gives an overall presentation of the most important aspects of quantum field theory, leading to its macroscopic manifestations, as in the formation of ordered structures. The list of topics, all covered in full detail and easy-to-follow steps, is really impressive. It includes the general structure of quantum mechanics and quantum field theory, the role of the inequivalent representations of the commutation relations, the spontaneous breakdown of symmetry with the consequent phenomenon of dynamical rearrangement of symmetry, quantum field theory at nonzero temperature, boson condensation and topological defects, dissipative quantum systems. The main features of the presentation rely on very simple and powerful unifying principles, given by the intermixing of symmetry and dynamics, under the general texture of quantum coherence. Most of the chapters share the typical flavor of the very intense personal research carried by the authors during the years, but the style of presentation is always perfectly coherent, and all topics are presented in a mature and well-organized way. I think that the book will be most useful for graduate students who are willing to be engaged in the fascinating task of exploring the full potentiality of quantum field theory in explaining the emergence of ordering at the macroscopic level, from the large-scale structure of the universe, to the ordering of biological systems. Of course, active researchers in all formation stages, but even mature scientists, will appreciate the intellectual depth and the scientific efficacy that the authors have transfused in their work.”Francesco Guerra Sapienza University of Rome, Italy “This book gives a very thorough treatment of a range of topics that are of increasing importance, from a rather unusual, and very instructive, point of view.”Tom W Kibble Imperial College London, UK “This book succeeds in helping the reader to understand how the macroscopic properties are generated out of quantum dynamics in the QFT framework. The level is adequate for graduate students with a basic knowledge of QFT.”Mathematical Reviews
