Principal Bundles The Classical Case /

• Main Author: Sontz, Stephen Bruce (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Universitext,
• Subjects: Mathematics.; Harmonic analysis.; Quantum computers.; Mathematical physics.; Mathematical Physics.; Quantum Computing.; Abstract Harmonic Analysis.

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, t...

Table of Contents:

• Introduction
• Basics of Manifolds
• Vector Bundles
• Vectors and Covectors
• Differential Forms
• Lie Derivatives
• Lie Groups
• Frobenius Theorem
• Principle Bundles
• Connections on Principle Bundles
• Curvature of a Connection
• Classical Electromagnetism
• Yang-Mills Theory
• Gauge Theory
• The Dirac Monopole
• Instantons
• What Next?
• Discussion of the Exercises.