Search results for: geometric-techniques-in-gauge-theories

Geometric Techniques in Gauge Theories

Author : R. Martini
File Size : 81.77 MB
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Geometric Techniques in Gauge Theories

Author : R. Martini
File Size : 64.87 MB
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Geometric Techniques in Gauge Theories

Author :
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Lecture Notes in Mathematics

Author :
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Advanced Geometric Techniques in Gauge Theory

Author :
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Finsler Geometry Relativity and Gauge Theories

Author : G.S. Asanov
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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.

Geometric Representation Theory and Gauge Theory

Author : Alexander Braverman
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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.

Differential Geometric Methods in Mathematical Physics

Author : Pedro L. Garcia
File Size : 71.37 MB
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The focal topic of the 14th International Conference on Differential Geometric Methods was that of mathematical problems in classical field theory and the emphasis of the resulting proceedings volume is on superfield theory and related topics, and classical and quantized fields.

Twistor Geometry and Field Theory

Author : R. S. Ward
File Size : 76.42 MB
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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.

Advances in Geometric Analysis

Author : Stanisław Janeczko
File Size : 48.43 MB
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Geometrical and Topological Methods in Gauge Theories

Author : Canadian Mathematical Congress (Society)
File Size : 66.6 MB
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Fiber Bundle Techniques in Gauge Theories

Author : W. Drechsler
File Size : 33.72 MB
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Geometric Methods for Quantum Field Theory

Author : Hernan Ocampo
File Size : 37.76 MB
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Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, SeibergOCoWitten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist''s and the mathematician''s perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents: Lectures: Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher); Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi); Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann); Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski); Renormalized Traces as a Geometric Tool (S Paycha); Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun); An Introduction to Seiberg-Witten Theory (H Ocampo); Short Communications: Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona); Multiplicative Anomaly for the e-Regularized Determinant (C Ducourtioux); On Cohomogeneity One Riemannian Manifolds (S M B Kashani); A Differentiable Calculus on the Space of Loops and Connections (M Reiris); Quantum Hall Conductivity and Topological Invariants (A Reyes); Determinant of the Dirac Operator Over the Interval [0, ] (F Torres-Ardila). Readership: Mathematicians and physicists."

Geometry Topology and Physics

Author : Mikio Nakahara
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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 of Low Dimensional Manifolds Volume 1 Gauge Theory and Algebraic Surfaces

Author : LMS Durham Symposium (1989)
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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.

Geometric and Topological Methods for Quantum Field Theory

Author : Alexander Cardona
File Size : 35.83 MB
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"Based on lectures given at the renowed Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics"--

Geometric Methods for Quantum Field Theory

Author : Hernan Ocampo
File Size : 25.5 MB
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Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg–Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents:Lectures:Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher)Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi)Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann)Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski)Renormalized Traces as a Geometric Tool (S Paycha)Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun)An Introduction to Seiberg-Witten Theory (H Ocampo)Short Communications:Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona)Multiplicative Anomaly for the ς-Regularized Determinant (C Ducourtioux)On Cohomogeneity One Riemannian Manifolds (S M B Kashani)A Differentiable Calculus on the Space of Loops and Connections (M Reiris)Quantum Hall Conductivity and Topological Invariants (A Reyes)Determinant of the Dirac Operator Over the Interval [0,β] (F Torres-Ardila) Readership: Mathematicians and physicists. Keywords:Reviews:“Many texts in theoretical physics do not contain a rigorous account of the mathematics they employ. However, this text does, and it omits no steps in the logic, thus making it very accessible to the mathematical community. Also it emphasizes physics, providing a link between the two disciplines which one rarely finds in a text.”Contemporary Physics

Modern Differential Geometry in Gauge Theories

Author : Anastasios Mallios
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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

Interdisciplinarity

Author : Julie Thompson Klein
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In this volume, Julie Klein provides the first comprehensive study of the modern concept of interdisciplinarity, supplementing her discussion with the most complete bibliography yet compiled on the subject. Spanning the social sciences, natural sciences, humanities, and professions, her study is a synthesis of existing scholarship on interdisciplinary research, education and health care. Klein argues that any interdisciplinary activity embodies a complex network of historical, social, psychological, political, economic, philosophical, and intellectual factors. Whether the context is a short-ranged instrumentality or a long-range reconceptualization of the way we know and learn, the concept of interdisciplinarity is an important means of solving problems and answering questions that cannot be satisfactorily addressed using singular methods or approaches.

Quantum Geometry

Author : Margaret Prugovecki
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This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.