Maxwell Fields, Volume I
Buch, Englisch, 293 Seiten, Format (B × H): 156 mm x 233 mm, Gewicht: 406 g
ISBN: 978-0-8176-4378-2
Verlag: Birkhauser Boston
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.
Fachgebiete
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
- Naturwissenschaften Physik Physik Allgemein Experimentalphysik
- Naturwissenschaften Physik Elektromagnetismus Elektrizität, Elektrodynamik
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Naturwissenschaften Physik Quantenphysik Teilchenphysik
- Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
Weitere Infos & Material
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.
