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. Nabertakes 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 mathematical 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. Iwould go over both volumes thoroughly and make some minor changes in terminology and notation and correct any errors I find. In this newedition, a chapter on Singular Homology will be added as well as minor changes in notation and terminology throughout and some sections have been rewrittenor omitted. Reviews of First Edition: “It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics...Naber combines a knowledge of his subject with an excellent informal writing style.' (NZMS Newletter) '...this book should be very interesting for mathematicians and physicists (as well as other scientists) who are concerned withgauge theories.' (Zentralblatt Fuer Mathematik) Detailed calculations of a number of concrete examples Written for both mathematicians who want to see something of the applications of topology and geometry to modern physics Written for physicists who want to see the foundations of their subject treated with mathematical rigor INDICE: Contents: Preface.- Physical and geometrical motivation 1 Topological spaces.- Homotopy groups.- Principal bundles.- Differentiable manifolds and matrix Lie groups.- Gauge fields and Instantons. Appendix. References. Index.
- ISBN: 978-1-4419-7253-8
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 440
- Fecha Publicación: 29/10/2010
- Nº Volúmenes: 1
- Idioma: Inglés