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Modern Differential Geometry in Gauge Theories: Yang-Mills Fields, Volume II
Tag	Description
020	$a9780817646349
082	$a516.36
099	$aOnline Resource: Birkhäuser
100	$aMallios, Anastasios.
245	$aModern Differential Geometry in Gauge Theories$h[Ebook]$bYang-Mills Fields, Volume II$cby Anastasios Mallios.
250	$a1.st ed.
260	$aBoston$bBirkhäuser$c2010.
300	$bonline resource.
336	$atext
338	$aonline resource
505	$aGeneral Preface -- Preface to Volume II -- Acknowledgments -- Contents of Volume I -- Part II Yang-Mills Theory: General Theory -- 1 Abstract Yang-Mills Theory -- 2 Moduli Spaces of A-Connections of Yang-Mills Fields -- 3 Geometry of Yang-Mills A-Connections -- Part III General Relativity -- 4 General Relativity, as a Gauge Theory. Singularities -- References -- Index of Notation -- Index.
520	$aDifferential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the authorâs 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.
538	$aOnline access is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
856	$uhttp://dx.doi.org/10.1007/978-0-8176-4634-9