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Author : R. Martini
Publisher : Springer
ISBN 13 : 3540391924
Total Pages : 231 pages
Book Rating : 4.5/5 (43 download)
Download or read book Geometric Techniques in Gauge Theories written by R. Martini and published by Springer. This book was released on 2006-11-14 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lance Bailey
Publisher : Nova Science Publishers
ISBN 13 : 9781634835466
Total Pages : 0 pages
Book Rating : 4.8/5 (354 download)
Download or read book Gauge Theories and Differential Geometry written by Lance Bailey and published by Nova Science Publishers. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book revisits the mathematical foundations of thermodynamics and gauge theory by using new differential geometric methods coming from the formal theory of systems of partial differential equations and Lie pseudogroups. The gauge theory of gravity is also established, in which spinorial and ventorial matter fields serve as gravitating sources. The potential applications of the present gauge theory of gravity, including quantum-vacuum-energy gravity, cosmological constant problem and gravity-gauge unification is also addressed. The third chapter focuses on a gravitational gauge theory with spin connection and vierbein as fundamental variables of gravity. Next, the place and physical significance of Poincaré gauge theory of gravity (PGTG) in the framework of gauge approach to gravitation is discussed. A cutoff regularization method in gauge theory is discussed in Chapter Five. The remaining chapters in the book focus on differential geometry, in particular, the authors show how fractional differential derived from fractional difference provides a basis to expand a theory of fractional differential geometry which would apply to non-differentiable manifolds; a review of the infinitesimal Baker-Campbell-Hausdorff formula is provided and the book concludes with a short communication where the authors focus on local stability, and describe how this leads naturally into the question of finite-time singularities and generalized soliton solutions.
Author : Alexander Braverman
Publisher : Springer Nature
ISBN 13 : 303026856X
Total Pages : 137 pages
Book Rating : 4.0/5 (32 download)
Download or read book Geometric Representation Theory and Gauge Theory written by Alexander Braverman and published by Springer Nature. This book was released on 2019-11-22 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.
Author : G.S. Asanov
Publisher : Springer
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.:/5 (49 download)
Download or read book Finsler Geometry, Relativity and Gauge Theories written by G.S. Asanov and published by Springer. This book was released on 1985 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian geometry justify the attempt to systematize the basic techniques for extending general relativity on the basis of Finsler geometry. It is this endeavour that forms the subject matter of the present book. Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to elucidate in this book. The book has been written in such a way that the reader acquainted with the methods of tensor calculus and linear algebra at the graduate level can use it as a manual of Finslerian techniques orientable to applications in several fields. The problems attached to the chapters are also intended to serve this purpose. This notwithstanding, whenever we touch upon the Finslerian refinement or generalization of physical concepts, we assume that the reader is acquainted with these concepts at least at the level of the standard textbooks, to which we refer him or her.
Author : Yuri Makeenko
Publisher : Cambridge University Press
ISBN 13 : 1009402056
Total Pages : 433 pages
Book Rating : 4.0/5 (94 download)
Download or read book Methods of Contemporary Gauge Theory written by Yuri Makeenko and published by Cambridge University Press. This book was released on 2023-07-31 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernard F. Schutz
Publisher : Cambridge University Press
ISBN 13 : 1107268141
Total Pages : 272 pages
Book Rating : 4.1/5 (72 download)
Download or read book Geometrical Methods of Mathematical Physics written by Bernard F. Schutz and published by Cambridge University Press. This book was released on 1980-01-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Author : M. Göckeler
Publisher : Cambridge University Press
ISBN 13 : 9780521378215
Total Pages : 248 pages
Book Rating : 4.3/5 (782 download)
Download or read book Differential Geometry, Gauge Theories, and Gravity written by M. Göckeler and published by Cambridge University Press. This book was released on 1989-07-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.
Author : Kishore B. Marathe
Publisher : North Holland
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Mathematical Foundations of Gauge Theories written by Kishore B. Marathe and published by North Holland. This book was released on 1992 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. theoretical physics and pure and applied mathematics who are acquainted with the elements of the theory of differential manifolds. It enables the reader to apply this theory to gauge theories and to understand the role of gauge theories in high energy physics, gravitation theory and electromagnetism.
Author : L. Mangiarotti
Publisher : World Scientific
ISBN 13 : 9789810236038
Total Pages : 376 pages
Book Rating : 4.2/5 (36 download)
Download or read book Gauge Mechanics written by L. Mangiarotti and published by World Scientific. This book was released on 1998 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. The gauge formulation of classical mechanics is extended to quantum mechanics under different reference frames. Special topics on geometric BRST mechanics, relativistic mechanics and others, together with many examples, are also dealt with.
Author : Heinz J Rothe
Publisher : World Scientific
ISBN 13 : 9814602302
Total Pages : 397 pages
Book Rating : 4.8/5 (146 download)
Download or read book Lattice Gauge Theories: An Introduction written by Heinz J Rothe and published by World Scientific. This book was released on 1992-01-29 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.
Author : Ta-Pei Cheng
Publisher : Oxford University Press
ISBN 13 : 0192652249
Total Pages : 549 pages
Book Rating : 4.1/5 (926 download)
Download or read book Gauge Theory of Elementary Particle Physics written by Ta-Pei Cheng and published by Oxford University Press. This book was released on 1994-08-02 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a practical introduction to the principal ideas in gauge theory and their applications to elementary particle physics. It explains technique and methodology with simple exposition backed up by many illustrative examples. Derivations, some of well known results, are presented in sufficient detail to make the text accessible to readers entering the field for the first time. The book focuses on the strong interaction theory of quantum chromodynamics and the electroweak interaction theory of Glashow, Weinberg, and Salam, as well as the grand unification theory, exemplified by the simplest SU(5) model. Not intended as an exhaustive survey, the book nevertheless provides the general background necessary for a serious student who wishes to specialize in the field of elementary particle theory. Physicists with an interest in general aspects of gauge theory will also find the book highly useful.
Author : Mikio Nakahara
Publisher : Taylor & Francis
ISBN 13 : 1420056948
Total Pages : 596 pages
Book Rating : 4.4/5 (2 download)
Download or read book Geometry, Topology and Physics written by Mikio Nakahara and published by Taylor & Francis. This book was released on 2018-10-03 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Rodolfo Gambini
Publisher : Cambridge University Press
ISBN 13 : 9780521654753
Total Pages : 344 pages
Book Rating : 4.6/5 (547 download)
Download or read book Loops, Knots, Gauge Theories and Quantum Gravity written by Rodolfo Gambini and published by Cambridge University Press. This book was released on 2000-07-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed in detail. Following chapters move on to consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.
Author : Chris Doran
Publisher : Cambridge University Press
ISBN 13 : 1139643142
Total Pages : 647 pages
Book Rating : 4.1/5 (396 download)
Download or read book Geometric Algebra for Physicists written by Chris Doran and published by Cambridge University Press. This book was released on 2007-11-22 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.
Author : Sylvie Paycha
Publisher : American Mathematical Soc.
ISBN 13 : 0821840622
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Sylvie Paycha and published by American Mathematical Soc.. This book was released on 2007 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
Author : R. S. Ward
Publisher : Cambridge University Press
ISBN 13 : 9780521422680
Total Pages : 534 pages
Book Rating : 4.4/5 (226 download)
Download or read book Twistor Geometry and Field Theory written by R. S. Ward and published by Cambridge University Press. This book was released on 1990 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.
Author : Yuji Tachikawa
Publisher : Springer
ISBN 13 : 331908822X
Total Pages : 236 pages
Book Rating : 4.3/5 (19 download)
Download or read book N=2 Supersymmetric Dynamics for Pedestrians written by Yuji Tachikawa and published by Springer. This book was released on 2014-10-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.
