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
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Table of contents (5 chapters)
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Front Matter
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Maxwell Fields: General Theory
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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. 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.
Authors and Affiliations
Bibliographic Information
Book Title: Modern Differential Geometry in Gauge Theories
Book Subtitle: Maxwell Fields, Volume I
Authors: Anastasios Mallios
DOI: https://doi.org/10.1007/0-8176-4474-1
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkh�user Boston 2006
Softcover ISBN: 978-0-8176-4378-2Published: 14 December 2005
eBook ISBN: 978-0-8176-4474-1Published: 27 July 2006
Edition Number: 1
Number of Pages: XVII, 293
Topics: Differential Geometry, Mathematical Methods in Physics, Field Theory and Polynomials, Elementary Particles, Quantum Field Theory, Classical Electrodynamics, Global Analysis and Analysis on Manifolds