Modern Differential Geometry in Gauge Theories

Yang-Mills Fields, Volume II
2010. Auflage 2009
ISBN: 978-0-8176-4379-9
Verlag: Springer Nature Singapore

Buch, Englisch, 234 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 378 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Mallios, Anastasios

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Naturwissenschaften Physik Elektromagnetismus Elektrizität, Elektrodynamik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik

Inhaltsverzeichnis

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.