000			03781nam a22005775i 4500
001			978-0-8176-4474-1
003			DE-He213
005			20161121231029.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817644741 _9978-0-8176-4474-1
024	7		_a10.1007/0-8176-4474-1 _2doi
050		4	_aQA641-670
072		7	_aPBMP _2bicssc
072		7	_aMAT012030 _2bisacsh
082	0	4	_a516.36 _223
100	1		_aMallios, Anastasios. _eauthor.
245	1	0	_aModern Differential Geometry in Gauge Theories _h[electronic resource] : _bMaxwell Fields, Volume I / _cby Anastasios Mallios.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aXVII, 293 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aMaxwell 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.
520			_aDifferential 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.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aField theory (Physics).
650		0	_aGlobal analysis (Mathematics).
650		0	_aManifolds (Mathematics).
650		0	_aDifferential geometry.
650		0	_aPhysics.
650		0	_aOptics.
650		0	_aElectrodynamics.
650		0	_aElementary particles (Physics).
650		0	_aQuantum field theory.
650	1	4	_aMathematics.
650	2	4	_aDifferential Geometry.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aField Theory and Polynomials.
650	2	4	_aElementary Particles, Quantum Field Theory.
650	2	4	_aOptics and Electrodynamics.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817643782
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4474-1
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507523 _d507523