Gauge Theory and Variational Principles

This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.
Starting with an examination of principal fiber bundles and connections, the text explores curvature
particle fields, Lagrangians, and gauge invariance
Lagrange's equation for particle fields
and the inhomogeneous field equation. Additional topics include free Dirac electron fields
interactions
calculus on frame bundle
and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.