<p>This is a book on topology and geometry and, like any books on subjects as vast as these, it has a point-of-view that guided the selection of topics. Naber takes the view 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 book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathemtical models of these notions. We ask the reader to come to us with some vague notion of what an electromagnetic field might be, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, a solid background in real analysis and linear algebra and 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 S4 with instanton number -1.</p>

Topology, Geometry and Gauge fields: Foundations (Texts in Applied Mathematics)

Science & Math

Gregory L. Naber

Mathematics

Springer

A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.

Topology, Geometry, and Gauge Fields: Interactions (Applied Mathematical Sciences)

See the best price to sell, buy, or rent books by Gregory L. Naber. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Gregory L. Naber

See the best price to sell, buy, or rent books by Gregory L. Naber. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Topology, Geometry and Gauge fields: Foundations (Texts in Applied Mathematics)

Topology, Geometry, and Gauge Fields: Interactions (Applied Mathematical Sciences)