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Principal Bundles, The Quantum Case

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This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material.

Author(s): Stephen Bruce Sontz
Series: Universitext
Publisher: Springer
Year: 2015

Language: English
Pages: 358
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