Many Body Physics Topology And Geometry

Author : Siddhartha Sen,Kumar Sankar Gupta
Publisher : World Scientific
Page : 220 pages
File Size : 51,9 Mb
Release : 2015-06-15
Category : Science
ISBN : 9789814678186

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Many-Body Physics, Topology and Geometry by Siddhartha Sen,Kumar Sankar Gupta Pdf

The book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics. With this aim, a brief intuitive introduction to many-body theory is given as a powerful qualitative tool for understanding complex systems. The important emergent concept of a quasiparticle is then introduced as a way to reduce a many-body problem to a single particle quantum problem. Examples of quasiparticles in graphene, superconductors, superfluids and in a topological insulator on a superconductor are discussed. The mathematical idea of self-adjoint extension, which allows short distance information to be included in an effective long distance theory through boundary conditions, is introduced through simple examples and then applied extensively to analyse and predict new physical consequences for graphene. The mathematical discipline of topology is introduced in an intuitive way and is then combined with the methods of differential geometry to show how the emergence of gapless states can be understood. Practical ways of carrying out topological calculations are described. Contents:OverviewMany-Body TheoryTopology and GeometryBoundary Conditions and Self-Adjoint ExtensionsElectronic Properties of Graphene Readership: Graduate students and researchers in condensed matter physics and mathematical physics. Key Features:Topics are of current interest, e.g. graphene, topological insulators, Majorana fermionsIs self-contained and provides all the background material necessary to understand the physical or mathematical concepts discussedPractical ways of using topology, self-adjoint extensions as well as ways of making qualitative estimates in physics are explained and then illustrated by examplesKeywords:Condensed Matter Physics;Topology;Differential Geometry;Many-Body Problem;Graphene;Self-Adjoint Extensions;K-Theory;Quasiparticles;Superconductivity;Superfluidity;Topological Insulator;Mathematical Physics

Author : Eike Bick
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 54,7 Mb
Release : 2005-01-18
Category : Mathematics
ISBN : 3540231250

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Topology and Geometry in Physics by Eike Bick Pdf

Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Author : Charles Nash,Siddhartha Sen
Publisher : Courier Corporation
Page : 302 pages
File Size : 50,7 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780486318363

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Topology and Geometry for Physicists by Charles Nash,Siddhartha Sen Pdf

Written by physicists for physics students, this text assumes no detailed background in topology or geometry. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. 1983 edition.

Author : Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta
Publisher : World Scientific
Page : 715 pages
File Size : 53,5 Mb
Release : 2005-01-27
Category : Science
ISBN : 9789814481144

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Geometric And Algebraic Topological Methods In Quantum Mechanics by Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta Pdf

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.

Author : Pires Antonio Sergio Teixeira
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 1901
Category : Electronic
ISBN : 1643273736

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Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics by Pires Antonio Sergio Teixeira Pdf

Author : Eike Bick,Frank Daniel Steffen
Publisher : Springer
Page : 362 pages
File Size : 50,5 Mb
Release : 2009-09-02
Category : Science
ISBN : 354080398X

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Topology and Geometry in Physics by Eike Bick,Frank Daniel Steffen Pdf

Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, sypersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.

Author : Chen Ning Yang,Mo-lin Ge,Yang-hui He
Publisher : World Scientific
Page : 231 pages
File Size : 40,7 Mb
Release : 2019-01-09
Category : Science
ISBN : 9789813278684

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Topology And Physics by Chen Ning Yang,Mo-lin Ge,Yang-hui He Pdf

'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.

Author : Edward Shuryak
Publisher : Princeton University Press
Page : 306 pages
File Size : 54,5 Mb
Release : 2018-11-27
Category : Science
ISBN : 9780691175607

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Quantum Many-Body Physics in a Nutshell by Edward Shuryak Pdf

The ideal textbook for a one-semester introductory course for graduate students or advanced undergraduates This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields—phenomena as well as theoretical tools—and does so in a simple and accessible way. Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle; in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses, and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid 3He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of quantized vortices in superfluids and superconductors to ensembles of colored (QCD) monopoles and instantons in the QCD vacuum. Proven in the classroom, Quantum Many-Body Physics in a Nutshell is the ideal textbook for a one-semester introductory course for graduate students or advanced undergraduates. Teaches students how quantum many-body systems work across many fields of physics Uses path integrals from the very beginning Features the easiest introduction to Feynman diagrams available Draws on the most recent findings, including trapped Fermi and Bose atomic gases Guides students from traditional systems, such as electron gas and nuclear matter, to more advanced ones, such as quark-gluon plasma and the QCD vacuum

Author : J. F. Sadoc
Publisher : World Scientific
Page : 318 pages
File Size : 42,7 Mb
Release : 1990
Category : Science
ISBN : 9810200897

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Geometry in Condensed Matter Physics by J. F. Sadoc Pdf

The subject of geometry has become an important ingredient in condensed matter physics. It appears not only to describe, but also to explain structures and their properties. There are two aspects to using geometry: the visual and intuitive understanding, which fosters an immediate grasp of the objects one studies, and the abstract tendency so well developed in the Riemannian manifold theory. Both aspects contribute to the same understanding when they are applied to the main problems occurring in condensed matter sciences. Sophisticated structures found in nature appear naturally as the result of simple constraints which are presented in geometrical terms. Blue phases, amorphous and glassy materials, Frank and Kasper Metals, quasi-crystals are approached in their complexity, using the simple principles of geometry. The relation between biology and liquid crystal sciences, the physics of membranes is a fundamental aspect presented in this book.

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 49,8 Mb
Release : 2010-09-24
Category : Mathematics
ISBN : 9781441972545

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Topology, Geometry and Gauge fields by Gregory L. Naber Pdf

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Author : Arkady L Kholodenko
Publisher : World Scientific
Page : 492 pages
File Size : 54,6 Mb
Release : 2013-05-03
Category : Mathematics
ISBN : 9789814412100

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Applications of Contact Geometry and Topology in Physics by Arkady L Kholodenko Pdf

Although contact geometry and topology is briefly discussed in V I Arnol'd's book “Mathematical Methods of Classical Mechanics ”(Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges “An Introduction to Contact Topology” (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph “Contact Geometry and Nonlinear Differential Equations” (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau–Lifshitz (L–L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L–L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L–L course some problems/exercises are formulated along the way and, again as in the L–L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L–L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text. Contents:Motivation and BackgroundFrom Ideal Magnetohydrodynamics to String and Knot TheoryAll About and Around Woltjer's TheoremTopologically Massive Gauge Theories and Force-Free FieldsContact Geometry and PhysicsSub-Riemannian Geometry, Heisenberg Manifolds and Quantum Mechanics of Landau LevelsAbrikosov Lattices, TGB Phases in Liquid Crystals and Heisenberg GroupSub-Riemannian Geometry, Spin Dynamics and Quantum-Classical Optimal ControlFrom Contact Geometry to Contact TopologyClosing Remarks:The Unreasonable Effectivenessof Contact Geometry and Topology in Physical SciencesAppendices:Heisenberg Group in the Context of Sub-Riemannian Geometry and Optimal ControlSub-Riemannian Dynamics of Josephson JunctionsQuantum Computers and Quantum Random WalksThe Measurement Protocol. Geometry and Topology of Entanglements Readership: Students in applied mathematics and theoretical physics. Keywords:Force-Free Fields;Contact and Sub-Riemannian Geometry;Optimal Control;Theoretical PhysicsKey Features:This book is the world's first book on contact/sub-Riemannian geometry and topology for physicistsUnlike books discussing mathematical methods for physicists, this book discusses physical problems first and only then uses new mathematics to solve these problems. Problems are selected from practically all branches of theoretical physicsThis is done with the purpose of demonstrating that contact geometry should be looked upon as a universal language/technical tool of theoretical physicsReviews: “This book is written in the style of the well-known Landau-Lifshitz multivolume course in theoretical physics and its prime goal, as the author puts it, is to show the diversity of applications of contact geometry and topology. I enjoyed reading this book, in which the author allows readers to see for themselves “the same forest behind different kinds of trees”. I strongly recommend this book to interested readers.” MathSciNet

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 41,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475768503

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Topology, Geometry, and Gauge Fields by Gregory L. Naber Pdf

A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.

Author : David Vanderbilt
Publisher : Cambridge University Press
Page : 395 pages
File Size : 46,6 Mb
Release : 2018-11
Category : Science
ISBN : 9781107157651

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Berry Phases in Electronic Structure Theory by David Vanderbilt Pdf

An introduction to the role of Berry phases in our modern understanding of the physics of electrons in solids.

Author : Mike Guidry,Yang Sun
Publisher : Cambridge University Press
Page : 665 pages
File Size : 47,9 Mb
Release : 2022-03-31
Category : Mathematics
ISBN : 9781316518618

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Symmetry, Broken Symmetry, and Topology in Modern Physics by Mike Guidry,Yang Sun Pdf

A pedagogical introduction to the modern applications of groups, algebras, and topology for undergraduate and graduate students in physics.

Author : Hal Tasaki
Publisher : Springer
Page : 509 pages
File Size : 42,9 Mb
Release : 2020-05-23
Category : Technology & Engineering
ISBN : 3030412644

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Physics and Mathematics of Quantum Many-Body Systems by Hal Tasaki Pdf

This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.