Supersymmetry And Trace Formulae

Author : Igor V. Lerner,Jonathan P. Keating,David E. Khmelnitskii
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461548751

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Supersymmetry and Trace Formulae by Igor V. Lerner,Jonathan P. Keating,David E. Khmelnitskii Pdf

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.

Author : Igor V Lerner,Jonathan P Keating,David E Khmelnitskii
Publisher : Unknown
Page : 420 pages
File Size : 41,6 Mb
Release : 1999-04-01
Category : Electronic
ISBN : 1461548764

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Supersymmetry and Trace Formulae by Igor V Lerner,Jonathan P Keating,David E Khmelnitskii Pdf

Author : PIGUET,SIBOLD
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 46,7 Mb
Release : 2013-03-08
Category : Science
ISBN : 9781468473261

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Renormalized Supersymmetry by PIGUET,SIBOLD Pdf

The present book grew out of lecture notes prepared for a "Cours du troisieme cycle de la Suisse Romande", 1983 in Lausanne. The original notes are considerably extended and brought up to date. In fact the book offers at many instances completely new derivations. Half-way between textbook and research monograph we believe it to be useful for students in elementary particle physics as well as for research workers in the realm of supersymmetry. In writing the book we looked back not only on ten years of super symmetry but also on ten years of our own life and work. We realize how deeply we are indebted to many friends and colleagues. Some shared our efforts, some helped and encouraged us, some provided the facili ties to work. Their list comprises at least C. Becchi, S. Bedding, P. Breitenlohner, T.E. Clark, S. Ferrara, R. Gatto, M. Jacob, W. Lang, J.H. Lowenstein, D. Maison, H. Nicolai, J. Prentki, A. Rouet, H. Ruegg, M. Schweda, R. Stora, J. Wess, W. Zimmermann, B. Zumino. During the last ten years we had the privilege to work at CERN (Geneva), Departement de Physique Theorique (University of Geneva), Institut fUr Theoretische Physik (University of Karlsruhe) and at the Max-Planck-Institut fUr Physik und Astrophysik (Munich) for which we are most grateful. Grate fully acknowledged is also the support we received by "the Swiss National Science Foundation" (O.P.), the "Deutsche Forschungsgemeinschaft" (Heisenberg-Fellowship; K.S.)

Author : Bijan Kumar Bagchi
Publisher : CRC Press
Page : 242 pages
File Size : 44,5 Mb
Release : 2000-09-21
Category : Science
ISBN : 1420035819

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Supersymmetry In Quantum and Classical Mechanics by Bijan Kumar Bagchi Pdf

Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods. Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.

Author : Allen Hirshfeld
Publisher : World Scientific
Page : 216 pages
File Size : 40,9 Mb
Release : 2012
Category : Science
ISBN : 9781848167988

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The Supersymmetric Dirac Equation by Allen Hirshfeld Pdf

The solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book. Analysis of the concept of eccentricity of the orbits turns out to be essential to understanding the relation of the classical and quantum mechanical models. The opportunity is taken to relive the great moments of physics: From Kepler''s discovery of the laws of motion of the planets, the development is traced through the Dirac equation up to modern advances, which bring the concepts of supersymmetry to bear on the derivation of the solutions.

Author : Christian Grosche
Publisher : World Scientific
Page : 388 pages
File Size : 49,8 Mb
Release : 2013-07-26
Category : Science
ISBN : 9789814460095

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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

Author : Fred Cooper,Avinash Khare,Uday Pandurang Sukhatme
Publisher : World Scientific
Page : 226 pages
File Size : 52,8 Mb
Release : 2001
Category : Science
ISBN : 9810246129

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Supersymmetry in Quantum Mechanics by Fred Cooper,Avinash Khare,Uday Pandurang Sukhatme Pdf

This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by students in advanced undergraduate quantum mechanics courses. Problems have been given at the end of each chapter, along with complete solutions to all the problems. The text also includes material of interest in current research not usually discussed in traditional courses on quantum mechanics, such as the connection between exact solutions to classical solution problems and isospectral quantum Hamiltonians, and the relation to the inverse scattering problem.

Author : Christian Grosche
Publisher : World Scientific
Page : 389 pages
File Size : 51,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814460088

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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.

Author : Florentin Smarandache,V. Christianto
Publisher : Infinite Study
Page : 516 pages
File Size : 43,8 Mb
Release : 2007
Category : Science
ISBN : 9788190219099

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Quantization in Astrophysics, Brownian Motion, and Supersymmetry by Florentin Smarandache,V. Christianto Pdf

Author : Michel Planat
Publisher : MDPI
Page : 206 pages
File Size : 46,5 Mb
Release : 2021-01-20
Category : Computers
ISBN : 9783039366866

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Number Theory and Symmetry by Michel Planat Pdf

According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.

Author : John Forbes Nash, Jr.,Michael Th. Rassias
Publisher : Springer
Page : 543 pages
File Size : 49,5 Mb
Release : 2016-07-05
Category : Mathematics
ISBN : 9783319321622

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Open Problems in Mathematics by John Forbes Nash, Jr.,Michael Th. Rassias Pdf

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Author : Yvan Saint-Aubin,Luc Vinet
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 41,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781475736717

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Theoretical Physics at the End of the Twentieth Century by Yvan Saint-Aubin,Luc Vinet Pdf

Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first. Young physicists will find in these chapters pedagogical introductions to subjects currently active in theoretical physics, and more seasoned physicists will find a chance to share the excitement of fields outside their immediate research interests.

Author : Konstantin Efetov
Publisher : Cambridge University Press
Page : 470 pages
File Size : 40,9 Mb
Release : 1999-09-13
Category : Mathematics
ISBN : 0521663822

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Supersymmetry in Disorder and Chaos by Konstantin Efetov Pdf

This book provides a comprehensive treatment of the ideas and applications of supersymmetry.

Author : Michael Dine
Publisher : Cambridge University Press
Page : 507 pages
File Size : 54,7 Mb
Release : 2023-01-31
Category : Science
ISBN : 9781009290920

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Supersymmetry and String Theory by Michael Dine Pdf

This text is an introduction to the fields of experimental and theoretical particle physics and cosmology. The book focuses on three principal areas: supersymmetry, string theory, and astrophysics and cosmology. The chapters on supersymmetry introduce the basics of supersymmetry and its phenomenology, and cover dynamics, dynamical supersymmetry breaking, and electric-magnetic duality. The book then introduces general relativity and the big bang theory, and the basic issues in inflationary cosmologies. The section on string theory discusses the spectra of known string theories, and the features of their interactions. Material added in the second edition includes the pivotal Higgs discovery and the results of the WMAP and Planck experiments. This book will be of great interest to graduates and researchers in the fields of particle theory, string theory, astrophysics, and cosmology. It has been reissued as an Open Access publication on Cambridge Core.

Author : Asim Gangopadhyaya,Jeffry V. Mallow,Constantin Rasinariu
Publisher : World Scientific
Page : 291 pages
File Size : 49,6 Mb
Release : 2011
Category : Science
ISBN : 9789814313094

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Supersymmetric Quantum Mechanics by Asim Gangopadhyaya,Jeffry V. Mallow,Constantin Rasinariu Pdf

This is the first such text which will be directed to undergraduates. Our approach is to provide a self-contained exposition, which begins with a review of the relevant introductory quantum mechanics, then segues into SUSYQM. We concentrate on the essentials, both in the chapters developing the architecture, and in the later chapters of applications. While the text is designed to be accessible to undergraduate students, it should also be useful to graduate students and to researchers in the field. The text contains a large selection of examples and problems that illustrate the ideas and their applications. It is richly illustrated with figures that we have designed and produced. We have selected an attractive and relevant list of topics.