04378nam 22007095 450 991025429490332120200704235445.097833196843839783319684390 (ebook)10.1007/978-3-319-68439-0(DE-He213)978-3-319-68439-0(CKB)4100000001381584(MiAaPQ)EBC6314446(MiAaPQ)EBC5591722(Au-PeEL)EBL5591722(OCoLC)1015676520(PPN)222228180(EXLCZ)99410000000138158420171208d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierMathematical Gauge Theory[electronic resource] With Applications to the Standard Model of Particle Physics /by Mark J.D. Hamilton1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XVIII, 658 p. 40 illus.)Universitext,0172-5939Part I Mathematical foundations -- 1 Lie groups and Lie algebras: Basic concepts -- 2 Lie groups and Lie algebras: Representations and structure theory -- 3 Group actions -- 4 Fibre bundles -- 5 Connections and curvature -- 6 Spinors -- Part II The Standard Model of elementary particle physics -- 7 The classical Lagrangians of gauge theories -- 8 The Higgs mechanism and the Standard Model -- 9 Modern developments and topics beyond the Standard Model -- Part III Appendix -- A Background on differentiable manifolds -- B Background on special relativity and quantum field theory -- References -- Index.The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.Universitext,0172-5939Manifolds (Mathematics)Complex manifoldsElementary particles (Physics)Quantum field theoryPhysicsTopological groupsLie groupsManifolds and Cell Complexes (incl. Diff.Topology)https://scigraph.springernature.com/ontologies/product-market-codes/M28027Elementary Particles, Quantum Field Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P23029Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Manifolds (Mathematics).Complex manifolds.Elementary particles (Physics).Quantum field theory.Physics.Topological groups.Lie groups.Manifolds and Cell Complexes (incl. Diff.Topology).Elementary Particles, Quantum Field Theory.Mathematical Methods in Physics.Topological Groups, Lie Groups.539.72Hamilton Mark J.Dauthttp://id.loc.gov/vocabulary/relators/aut959448MiAaPQMiAaPQMiAaPQ9910254294903321Mathematical Gauge Theory2174094UNINA