TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Modern Differential Geometry in Gauge Theories: Maxwell Fields, Volume I 
SN  - 9780817644741
AV  - QA641-670 
U1  - 516.36 23
PY  - 2006///
CY  - Boston, MA
PB  - Birkhuser Boston
KW  - Mathematics
KW  - Field theory (Physics)
KW  - Global analysis
KW  - Global differential geometry
KW  - Mathematical physics
KW  - Quantum theory
KW  - Electrodynamics
KW  - Differential Geometry
KW  - Mathematical Methods in Physics
KW  - Field Theory and Polynomials
KW  - Elementary Particles, Quantum Field Theory
KW  - Classical Electrodynamics, Wave Phenomena
KW  - Global Analysis and Analysis on Manifolds
N1  - Maxwell Fields: General Theory -- The Rudiments of Abstract Differential Geometry -- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnicks Correspondence Principle -- Electromagnetism -- Cohomological Classification of Maxwell and Hermitian Maxwell Fields -- Geometric Prequantization; ZDB-2-SMA
N2  - Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the authors 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 YangMills 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
UR  - http://dx.doi.org/10.1007/0-8176-4474-1
ER  -