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

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 construction blocks:
- Geometry and topology of fibre bundles,
- Clifford algebras, spin buildings and Dirac operators,
- Gauge theory.
Written within the form of a mathematical textbook, it combines a accomplished presentation of the mathematical foundations with a dialogue of a number of complicated themes in gauge theory.
The first development block features a variety of particular themes, like invariant connections, common connections, H-structures and the Postnikov approximation of classifying spaces.
Given the good significance of Dirac operators in gauge conception, an entire evidence of the Atiyah-Singer Index Theorem is gifted. The gauge conception half comprises the learn of Yang-Mills equations (including the speculation of instantons and the classical balance analysis), the dialogue of assorted versions with topic fields (including magnetic monopoles, the Seiberg-Witten version and dimensional relief) and the research of the constitution of the gauge orbit house. 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 publication is addressed either to physicists and mathematicians. it really is meant to be available to scholars ranging from a graduate level.

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Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields (Theoretical and Mathematical Physics)

The ebook is dedicated to the learn of the geometrical and topological constitution of gauge theories. It includes the subsequent 3 construction blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin buildings and Dirac operators,- Gauge idea. Written within the type of a mathematical textbook, it combines a complete presentation of the mathematical foundations with a dialogue of numerous complex issues in gauge concept.

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