Differential Geometry and Mathematical Physics

Differential Geometry and Mathematical Physics

Author: Gerd Rudolph

Publisher: Springer

ISBN: 9789402409598

Category: Science

Page: 830

View: 819

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

Differential Geometry and Mathematical Physics
Language: en
Pages: 830
Authors: Gerd Rudolph, Matthias Schmidt
Categories: Science
Type: BOOK - Published: 2017-03-22 - Publisher: Springer

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive
Differential Geometry and Mathematical Physics
Language: en
Pages: 762
Authors: Gerd Rudolph, Matthias Schmidt
Categories: Science
Type: BOOK - Published: 2014-12-14 - Publisher: Springer

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics
An Introduction to Differential Geometry and Topology in Mathematical Physics
Language: en
Pages: 220
Authors: Wang Rong, Chen Yue
Categories: Mathematics
Type: BOOK - Published: 1999-01-18 - Publisher: World Scientific

This book gives an outline of the developments of differential geometry and topology in the twentieth century, especially those which will be closely related to new discoveries in theoretical physics. Contents:Differential Manifolds:Preliminary Knowledge and DefinitionsProperties and Operations of Tangent Vectors and Cotangent VectorsCurvature Tensors, Torsion Tensors, Covariant Differentials and Adjoint
Differential Geometry, Differential Equations, and Mathematical Physics
Language: en
Pages: 231
Authors: Maria Ulan, Eivind Schneider
Categories: Mathematics
Type: BOOK - Published: 2021-02-13 - Publisher: Birkhäuser

This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus,
Differential Geometry and Mathematical Physics
Language: en
Pages: 224
Authors: John K. Beem, Krishan L. Duggal, American Mathematical Society, Canadian Mathematical Society
Categories: Mathematics
Type: BOOK - Published: 1994 - Publisher: American Mathematical Soc.

This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities,