Overview
- Original, well-written work of interest
- Presents for the first time (physical) field theories written in sheaf-theoretic language
- Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments
- Author's mastery of the subject and the rigorous treatment of this text make it invaluable
- Includes supplementary material: sn.pub/extras
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Table of contents (4 chapters)
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Front Matter
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Yang–Mills Theory: General Theory
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Front Matter
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Yang–Mills Theory:General Theory
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General Relativity
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Front Matter
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Back Matter
Keywords
About this book
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.
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)Authors and Affiliations
Bibliographic Information
Book Title: Modern Differential Geometry in Gauge Theories
Book Subtitle: Yang–Mills Fields, Volume II
Authors: Anastasios Mallios
DOI: https://doi.org/10.1007/978-0-8176-4634-9
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkh�user Boston 2010
Softcover ISBN: 978-0-8176-4379-9Published: 05 November 2009
eBook ISBN: 978-0-8176-4634-9Published: 22 October 2009
Edition Number: 1
Number of Pages: XIX, 234
Number of Illustrations: 5 b/w illustrations
Topics: Differential Geometry, Mathematical Methods in Physics, Field Theory and Polynomials, Elementary Particles, Quantum Field Theory, Classical Electrodynamics, Global Analysis and Analysis on Manifolds