Modern Differential Geometry in Gauge Theories: Yang-Mills Fields, Volume II

by Anastasios Mallios

Overview

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications.

Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Volume 1 focused on Maxwell fields. Continuing in Volume II, the author extends the application of his sheaf-theoretic approach to Yang–Mills fields in general. The text contains a wealthof detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity.

Product Details

ISBN-13:	9780817643799
Publisher:	Birkhäuser Boston
Publication date:	11/05/2009
Series:	Progress in Mathematical Physics Series , #42
Edition description:	2010
Pages:	234
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Yang–Mills Theory:General Theory.- Abstract Yang#x2013;Mills Theory.- Moduli Spaces of -Connections of Yang#x2013;Mills Fields.- Geometry of Yang#x2013;Mills -Connections.- General Relativity.- General Relativity, as a Gauge Theory. Singularities.

Editorial Reviews

From the reviews:

“This book is the sequel to [Modern differential geometry in gauge theories. Vol. I: Maxwell fields. Boston, MA: Birkhäuser (2006; Zbl 1116.18006)], continuing the study of gauge theories in the framework of abstract differential geometry. It consists of four chapters. … All in all, the book is well written, and it is recommendable to novices and specialists.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1185, 2010)

From the Publisher