Modern Differential Geometry in Gauge Theories [electronic resource] :Maxwell Fields, Volume I / by Anastasios Mallios.
by Mallios, Anastasios [author.]; SpringerLink (Online service).
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BookPublisher: Boston, MA : Birkhäuser Boston, 2006.Description: XVII, 293 p. online resource.ISBN: 9780817644741.Subject(s): Mathematics | Field theory (Physics) | Global analysis | Global differential geometry | Mathematical physics | Quantum theory | Electrodynamics | Mathematics | Differential Geometry | Mathematical Methods in Physics | Field Theory and Polynomials | Elementary Particles, Quantum Field Theory | Classical Electrodynamics, Wave Phenomena | Global Analysis and Analysis on ManifoldsDDC classification: 516.36 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA641-670 (Browse shelf) | Available |
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| QA440-699 The Unity of Mathematics | QA370-380 Homogenization of Partial Differential Equations | QA440-699 Geometric Problems on Maxima and Minima | QA641-670 Modern Differential Geometry in Gauge Theories | QA21-27 The History of Approximation Theory | QA273.A1-274.9 Lagrangian Probability Distributions | QA641-670 Cycle Spaces of Flag Domains |
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.
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. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. The text 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.
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