Geometry Topology And Physics Second Edition
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Geometry Topology And Physics
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Author : Mikio Nakahara
language : en
Publisher: Taylor & Francis
Release Date : 2018-10-03
Geometry Topology And Physics written by Mikio Nakahara and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
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.
Geometry Topology And Physics Second Edition
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Author : Mikio Nakahara
language : en
Publisher: CRC Press
Release Date : 2003-06-04
Geometry Topology And Physics Second Edition written by Mikio Nakahara and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-04 with Mathematics categories.
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.
Geometry Topology And Physics
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Author : M. NAKAHARA
language : en
Publisher: Institute of Physics Publishing (GB)
Release Date : 1999
Geometry Topology And Physics written by M. NAKAHARA and has been published by Institute of Physics Publishing (GB) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
"Geometry, Topology and Physics is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics."--BOOK JACKET.
Topics In Contemporary Mathematical Physics Second Edition
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Author : Kai S Lam
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-09-17
Topics In Contemporary Mathematical Physics Second Edition written by Kai S Lam and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-17 with Science categories.
This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan-Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.
The 4d Spiral Spacetimes Toryx Helyx Prime Elements Of The Multiverse
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Author : Vladimir Ginzburg
language : en
Publisher: Lulu.com
Release Date : 2018-05-25
The 4d Spiral Spacetimes Toryx Helyx Prime Elements Of The Multiverse written by Vladimir Ginzburg and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-25 with Science categories.
This book describes abstract and applied mathematics of the unique properties of 4D spiral spacetimes called toryx and helyx. There is a good reason for studying the mathematics of these two spacetimes. Their unique properties provide them with a capability to be the prime elements of nature. In that capacity their potential role in nature would be comparable with a role of the DNA double helyces discovered by James Watson and Francis Crick in 1953. The DNA double helyces contain genetic codes defining the properties of both organic entities and living organisms, whereas both toryx and helyx contain generic codes defining the properties of matter and radiation entities of the Universe. Also similar are the locations of these codes. The genetic codes of DNA are located inside of cells of all organic entities and living organisms, whereas the generic codes of toryces and helyces reside inside of all elementary matter and radiation particles, the building blocks of the Universe.
Mathematical Tools For Physicists
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Author : Michael Grinfeld
language : en
Publisher: John Wiley & Sons
Release Date : 2015-01-12
Mathematical Tools For Physicists written by Michael Grinfeld and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-12 with Science categories.
The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.
Mathematics For Physicists
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Author : Alexander Altland
language : en
Publisher: Cambridge University Press
Release Date : 2019-02-14
Mathematics For Physicists written by Alexander Altland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Mathematics categories.
Introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.
Arithmetic And Geometry Around Quantization
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Author : Özgür Ceyhan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-12
Arithmetic And Geometry Around Quantization written by Özgür Ceyhan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-12 with Mathematics categories.
This volume comprises both research and survey articles originating from the conference on Arithmetic and Geometry around Quantization held in Istanbul in 2006. A wide range of topics related to quantization are covered, thus aiming to give a glimpse of a broad subject in very different perspectives.
Approximability Of Optimization Problems Through Adiabatic Quantum Computation
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Author : William Cruz-Santos
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Approximability Of Optimization Problems Through Adiabatic Quantum Computation written by William Cruz-Santos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is large enough, then the system remains close to its ground state. An AQC algorithm uses the adiabatic theorem to approximate the ground state of the final Hamiltonian that corresponds to the solution of the given optimization problem. In this book, we investigate the computational simulation of AQC algorithms applied to the MAX-SAT problem. A symbolic analysis of the AQC solution is given in order to understand the involved computational complexity of AQC algorithms. This approach can be extended to other combinatorial optimization problems and can be used for the classical simulation of an AQC algorithm where a Hamiltonian problem is constructed. This construction requires the computation of a sparse matrix of dimension 2n × 2n, by means of tensor products, where n is the dimension of the quantum system. Also, a general scheme to design AQC algorithms is proposed, based on a natural correspondence between optimization Boolean variables and quantum bits. Combinatorial graph problems are in correspondence with pseudo-Boolean maps that are reduced in polynomial time to quadratic maps. Finally, the relation among NP-hard problems is investigated, as well as its logical representability, and is applied to the design of AQC algorithms. It is shown that every monadic second-order logic (MSOL) expression has associated pseudo-Boolean maps that can be obtained by expanding the given expression, and also can be reduced to quadratic forms. Table of Contents: Preface / Acknowledgments / Introduction / Approximability of NP-hard Problems / Adiabatic Quantum Computing / Efficient Hamiltonian Construction / AQC for Pseudo-Boolean Optimization / A General Strategy to Solve NP-Hard Problems / Conclusions / Bibliography / Authors' Biographies
The Unique Properties Of 4d Spiral Spacetime Toryx
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Author : Vladimir Ginzburg
language : en
Publisher: Lulu.com
Release Date : 2017-08-31
The Unique Properties Of 4d Spiral Spacetime Toryx written by Vladimir Ginzburg and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-31 with Science categories.
According to the title of this book, the toryx is a four-dimensional (4D) spiral spacetime. It means its properties are described by three space plus one time parameters. Part 1 of this book presents properties of toryces in abstract mathematical terms. Part 2 shows several applications of toryces for mathematical modeling of properties of entities of both micro- and macro-worlds. This book further confirms a main proposition of the author's Universal Space Theory (UST) that the toryx has all attributes required to be a prime element of nature.