Gauge Field Theory And Complex Geometry

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Gauge Field Theory and Complex Geometry

Author : Yuri I. Manin
Publisher : Springer Science & Business Media
ISBN 13 : 9783540613787
Total Pages : 368 pages
Book Rating : 4.6/5 (137 download)

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Book Synopsis Gauge Field Theory and Complex Geometry by : Yuri I. Manin

Download or read book Gauge Field Theory and Complex Geometry written by Yuri I. Manin and published by Springer Science & Business Media. This book was released on 1997-05-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

Gauge Field Theory and Complex Geometry

Author : Yuri I. Manin
Publisher : Springer Science & Business Media
ISBN 13 : 3662073862
Total Pages : 357 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Gauge Field Theory and Complex Geometry by : Yuri I. Manin

Download or read book Gauge Field Theory and Complex Geometry written by Yuri I. Manin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

Gauge Field Theory and Complex Geometry

Author : Yuri I. Manin
Publisher : Springer
ISBN 13 : 9783662073872
Total Pages : 348 pages
Book Rating : 4.0/5 (738 download)

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Book Synopsis Gauge Field Theory and Complex Geometry by : Yuri I. Manin

Download or read book Gauge Field Theory and Complex Geometry written by Yuri I. Manin and published by Springer. This book was released on 2014-10-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

Conformal Field Theory with Gauge Symmetry

Author : Kenji Ueno
Publisher : American Mathematical Soc.
ISBN 13 : 0821840886
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Conformal Field Theory with Gauge Symmetry by : Kenji Ueno

Download or read book Conformal Field Theory with Gauge Symmetry written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 2008 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces withcoordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}1$.Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.

Differential Geometry, Gauge Theories, and Gravity

Author : M. Göckeler
Publisher : Cambridge University Press
ISBN 13 : 9780521378215
Total Pages : 248 pages
Book Rating : 4.3/5 (782 download)

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Book Synopsis Differential Geometry, Gauge Theories, and Gravity by : M. Göckeler

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.

Modern Differential Geometry in Gauge Theories

Author : Anastasios Mallios
Publisher : Springer Science & Business Media
ISBN 13 : 0817644741
Total Pages : 293 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Modern Differential Geometry in Gauge Theories by : Anastasios Mallios

Download or read book Modern Differential Geometry in Gauge Theories written by Anastasios Mallios and published by Springer Science & Business Media. This book was released on 2006-07-27 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable

Gauge Field Theory in Natural Geometric Language

Author : Daniel Canarutto
Publisher : Oxford University Press, USA
ISBN 13 : 0198861494
Total Pages : 362 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Gauge Field Theory in Natural Geometric Language by : Daniel Canarutto

Download or read book Gauge Field Theory in Natural Geometric Language written by Daniel Canarutto and published by Oxford University Press, USA. This book was released on 2020-10-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.

Topology, Geometry, and Gauge Fields

Author : Gregory Naber
Publisher : Springer Science & Business Media
ISBN 13 : 9780387949468
Total Pages : 428 pages
Book Rating : 4.9/5 (494 download)

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Book Synopsis Topology, Geometry, and Gauge Fields by : Gregory Naber

Download or read book Topology, Geometry, and Gauge Fields written by Gregory Naber and published by Springer Science & Business Media. This book was released on 1997-04-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Field Theory III: Gauge Theory

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
ISBN 13 : 3642224210
Total Pages : 1141 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Quantum Field Theory III: Gauge Theory by : Eberhard Zeidler

Download or read book Quantum Field Theory III: Gauge Theory written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 1141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

Strings, Gauge Fields, and the Geometry Behind

Author : Anton Rebhan
Publisher : World Scientific
ISBN 13 : 9814412554
Total Pages : 566 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Strings, Gauge Fields, and the Geometry Behind by : Anton Rebhan

Download or read book Strings, Gauge Fields, and the Geometry Behind written by Anton Rebhan and published by World Scientific. This book was released on 2012 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West.Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon.Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP.By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.

Geometric Representation Theory and Gauge Theory

Author : Alexander Braverman
Publisher : Springer Nature
ISBN 13 : 303026856X
Total Pages : 137 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Geometric Representation Theory and Gauge Theory by : Alexander Braverman

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.

Gauge Theory and Symplectic Geometry

Author : Jacques Hurtubise
Publisher : Springer Science & Business Media
ISBN 13 : 9401716676
Total Pages : 227 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Gauge Theory and Symplectic Geometry by : Jacques Hurtubise

Download or read book Gauge Theory and Symplectic Geometry written by Jacques Hurtubise and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.

Geometric Techniques in Gauge Theories

Author : R. Martini
Publisher : Springer
ISBN 13 : 3540391924
Total Pages : 231 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Geometric Techniques in Gauge Theories by : R. Martini

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:

Geometric Analysis and Applications to Quantum Field Theory

Author : Peter Bouwknegt
Publisher : Springer Science & Business Media
ISBN 13 : 1461200679
Total Pages : 213 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometric Analysis and Applications to Quantum Field Theory by : Peter Bouwknegt

Download or read book Geometric Analysis and Applications to Quantum Field Theory written by Peter Bouwknegt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.

Topology, Geometry, and Gauge Fields

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
ISBN 13 : 1475768508
Total Pages : 453 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Topology, Geometry, and Gauge Fields by : Gregory L. Naber

Download or read book Topology, Geometry, and Gauge Fields written by Gregory L. Naber and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces

Author : S. K. Donaldson
Publisher : Cambridge University Press
ISBN 13 : 0521399785
Total Pages : 277 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces by : S. K. Donaldson

Download or read book Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1990 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.

The Mathematical Foundations of Gauge Theories

Author : Kishore B. Marathe
Publisher : North Holland
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Mathematical Foundations of Gauge Theories by : Kishore B. Marathe

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.