Modern Differential Geometry in Gauge Theories

Maxwell Fields, Volume I
1. Auflage 2005
ISBN: 978-0-8176-4378-2
Verlag: Springer Nature B.V.

Buch, Englisch, 293 Seiten, Format (B × H): 156 mm x 233 mm, Gewicht: 406 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.

is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. Thetext contains a wealth of 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
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Elektromagnetismus Elektrizität, Elektrodynamik
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Inhaltsverzeichnis

Maxwell Fields: General Theory.- The Rudiments of Abstract Differential Geometry.- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnick’s Correspondence Principle.- Electromagnetism.- Cohomological Classification of Maxwell and Hermitian Maxwell Fields.- Geometric Prequantization.