This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles. While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.
Author(s): Stephen Bruce Sontz
Series: Universitext
Publisher: Springer
Year: 2015
Language: English
Pages: 285
Tags: Mathematical Physics; Quantum Computing; Abstract Harmonic Analysis
Front Matter....Pages i-xv
Introduction....Pages 1-5
Basics of Manifolds....Pages 7-29
Vector Bundles....Pages 31-48
Vectors, Covectors, and All That....Pages 49-57
Exterior Algebra and Differential Forms....Pages 59-79
Lie Derivatives....Pages 81-91
Lie Groups....Pages 93-103
The Frobenius Theorem....Pages 105-110
Principal Bundles....Pages 111-119
Connections on Principal Bundles....Pages 121-144
Curvature of a Connection....Pages 145-150
Classical Electromagnetism....Pages 151-172
Yang–Mills Theory....Pages 173-193
Gauge Theory....Pages 195-223
The Dirac Monopole....Pages 225-232
Instantons....Pages 233-246
What Next?....Pages 247-247
Back Matter....Pages 249-280
