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

By Gerd Rudolph,Matthias Schmidt

The ebook is dedicated to the examine of the geometrical and topological constitution of gauge theories. It involves the subsequent 3 construction blocks:
- Geometry and topology of fibre bundles,
- Clifford algebras, spin buildings and Dirac operators,
- Gauge theory.
Written within the sort of a mathematical textbook, it combines a entire presentation of the mathematical foundations with a dialogue of numerous complicated issues in gauge theory.
The first construction block contains 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 conception, an entire facts of the Atiyah-Singer Index Theorem is gifted. The gauge thought half includes the examine of Yang-Mills equations (including the idea of instantons and the classical balance analysis), the dialogue of varied versions with topic fields (including magnetic monopoles, the Seiberg-Witten version and dimensional aid) and the research of the constitution of the gauge orbit house. the ultimate bankruptcy is dedicated to components of quantum gauge conception 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's meant to be available to scholars ranging from a graduate level.

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