Read e-book online Differential Geometry and Mathematical Physics: Part II. PDF

By Gerd Rudolph,Matthias Schmidt

The publication is dedicated to the examine of the geometrical and topological constitution of gauge theories. It comprises the subsequent 3 development blocks:
- Geometry and topology of fibre bundles,
- Clifford algebras, spin buildings and Dirac operators,
- Gauge theory.
Written within the kind of a mathematical textbook, it combines a finished presentation of the mathematical foundations with a dialogue of a number of complicated themes in gauge theory.
The first development block incorporates a variety of particular themes, like invariant connections, common connections, H-structures and the Postnikov approximation of classifying spaces.
Given the nice value of Dirac operators in gauge concept, an entire evidence of the Atiyah-Singer Index Theorem is gifted. The gauge conception half comprises the research of Yang-Mills equations (including the idea of instantons and the classical balance analysis), the dialogue of assorted versions with topic fields (including magnetic monopoles, the Seiberg-Witten version and dimensional aid) and the research of the constitution of the gauge orbit area. the ultimate bankruptcy is dedicated to parts of quantum gauge concept together with the dialogue of the Gribov challenge, anomalies and the implementation of the non-generic gauge orbit strata within the framework of Hamiltonian lattice gauge theory.
The ebook is addressed either to physicists and mathematicians. it really is meant to be obtainable to scholars ranging from a graduate level.

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Read Online or Download Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields (Theoretical and Mathematical Physics) PDF

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Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields (Theoretical and Mathematical Physics) by Gerd Rudolph,Matthias Schmidt

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