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|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA641.SPR FCT 80960 (Browse shelf) | 1 | Available |
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| QA641.SPR FCT 102584 Il concetto di curvatura | QA641.SPR FCT 103606 Pseudo-riemannian homogeneous structures | QA641.SPR FCT 103649 Lectures and surveys on G2-manifolds and related topics | QA641.SPR FCT 80960 Modern differential geometry in Gauge theories | QA641.SPR FCT 80978 Higher structures in geometry and physics | QA641.SPR FCT 80994 Arithmetic and geometry around quantization | QA641.SPR FCT 81017 Representation theory and complex geometry |
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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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