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

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Posted on 2020-01-14, by books_lover.

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The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks: - Geometry and topology of fibre bundles, - Clifford algebras, spin structures and Dirac operators, - Gauge theory. Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory. The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Se

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

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