Topology, Geometry, and Gauge Fields

This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author's point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theory of physicists with the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) -connections on S[subscript 4] with instanton number -1.

First sentence: In this preliminary chapter we have gathered together a brief synopsis of those items from differential geometry upon which the main development of the text will be built.

Year

1997

Language

English

Publisher

Springer

Editions

1

Pages

464

ISBN

9780387989471

Data source: Wikidata