Geometry, Topology and Physics, Second Edition

Author: Mikio Nakahara

Publisher: CRC Press

ISBN: 9780750306065

Category: Mathematics

Page: 596

View: 6472


Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Structure of Space and the Submicroscopic Deterministic Concept of Physics

Author: Volodymyr Krasnoholovets

Publisher: CRC Press

ISBN: 1315341387

Category: Science

Page: 472

View: 1091


This book, Structure of Space and the Submicroscopic Deterministic Concept of Physics, completely formalizes fundamental physics by showing that all space, which consists of objects and distances, arises from the same origin: manifold of sets. A continuously organized mathematical lattice of topological balls represents the primary substrate named the tessellattice. All fundamental particles arise as local fractal deformations of the tessellattice. The motion of such particulate balls through the tessellattice causes it to deform neighboring cells, which generates a cloud of a new kind of spatial excitations named ‘inertons’. Thus, so-called "hidden variables" introduced in the past by de Broglie, Bohm and Vigier have acquired a sense of real quasiparticles of space.This theory of space unambiguously answers such challenging issues as: what is mass, what is charge, what is a photon, what is the wave psi-function, what is a neutrino, what are the nuclear forces, and so on. The submicroscopic concept uncovers new peculiar properties of quantum systems, especially the dynamics of particles within a section equal to the particle’s de Broglie wavelength, which are fundamentally impossible for quantum mechanics. This concept, thoroughly discussed in the book, allows one to study complex problems in quantum optics and quantum electrodynamics in detail, to disclose an inner world of particle physics by exposing the structure of quarks and nucleons in real space, and to derive gravity as the transfer of local deformations of space by inertons which in turn completely solves the problems of dark matter and dark energy. Inertons have revealed themselves in a number of experiments carried out in condensed media, plasma, nuclear physics and astrophysics, which are described in this book together with prospects for future studies in both fundamental and applied physics.

Superfluidity and Superconductivity

Author: D.R. Tilley,J Tilley

Publisher: CRC Press

ISBN: 9780750300339

Category: Science

Page: 240

View: 2838


Superfluidity and Superconductivity, Third Edition introduces the low-temperature phenomena of superfluidity and superconductivity from a unified viewpoint. The book stresses the existence of a macroscopic wave function as a central principle, presents an extensive discussion of macroscopic theories, and includes full descriptions of relevant experimental results throughout. This edition also features an additional chapter on high-temperature superconductors. With problems at the end of most chapters as well as the careful elaboration of basic principles, this comprehensive survey of experiment and theory provides an accessible and invaluable foundation for graduate students studying low-temperature physics as well as senior undergraduates taking specialized courses.

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Proceedings of the 2011 Villa de Leyva Summer School, Villa de Leyva, Colombia, 4-22 July 2011

Author: Sylvie Payche

Publisher: World Scientific

ISBN: 9814460052

Category: Science

Page: 378

View: 9795


Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Mathematics for Physics

A Guided Tour for Graduate Students

Author: Michael Stone,Paul Goldbart

Publisher: Cambridge University Press

ISBN: 0521854032

Category: Science

Page: 806

View: 5409


An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics - differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study.

Symmetry principles and magnetic symmetry in solid state physics

Author: S. J. Joshua

Publisher: Taylor & Francis


Category: Science

Page: 270

View: 837


Divided into two parts, the first half of this text covers all of the topics required for a complete understanding of the applications of group theory to solid state physics. It shows how symmetry arguments can be used to give detailed insight into the physical properties of crystals closely linked with structure.The second half of the book distinguishes it from other books on this subject by its treatment of symmetry properties of magnetic crystals at a level suitable for graduate students new to the field.

Introduction to Surface and Superlattice Excitations

Author: Michael .G. Cottam,D.R. Tilley

Publisher: CRC Press

ISBN: 9781420056914

Category: Science

Page: 516

View: 4646


Cottam and Tilley provide an introduction to the properties of wave-like excitations associated with surfaces and interfaces. The emphasis is on acoustic, optic and magnetic excitations, and apart from one section on liquid surfaces, the text concentrates on solids. The important topic of superlattices is also discussed, in which the different kinds of excitation are considered from a unified point of view. Throughout the book, the authors are careful to relate theory and experiment and all of the most important experimental techniques are described. The theoretical treatment assumes only a knowledge of undergraduate physics, except for Green function methods that are used in a few sections; these methods are developed in an appendix. The book also contains extensive references, enabling the reader to consult the research and review literature. Each of the main chapters contains problems to allow the reader to develop topics presented in the text.

Quantum Invariants

A Study of Knots, 3-manifolds, and Their Sets

Author: Tomotada Ohtsuki

Publisher: World Scientific

ISBN: 9789812811172

Category: Electronic books

Page: 508

View: 8151


This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."