Download Differential Geometry and Mathematical Physics: Part II. by Gerd Rudolph,Matthias Schmidt PDF

By Gerd Rudolph,Matthias Schmidt

The ebook is dedicated to the research of the geometrical and topological constitution of gauge theories. It comprises the next 3 development blocks:
- Geometry and topology of fibre bundles,
- Clifford algebras, spin constructions and Dirac operators,
- Gauge theory.
Written within the form of a mathematical textbook, it combines a complete presentation of the mathematical foundations with a dialogue of numerous complex subject matters in gauge theory.
The first development block incorporates a variety of particular issues, like invariant connections, common connections, H-structures and the Postnikov approximation of classifying spaces.
Given the nice significance of Dirac operators in gauge thought, a whole evidence of the Atiyah-Singer Index Theorem is gifted. The gauge thought half includes the learn of Yang-Mills equations (including the speculation of instantons and the classical balance analysis), the dialogue of assorted types with topic fields (including magnetic monopoles, the Seiberg-Witten version and dimensional relief) and the research of the constitution of the gauge orbit area. the ultimate bankruptcy is dedicated to components 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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