LEADER 04378nam 22007095 450 001 9910254294903321 005 20200704235445.0 010 $a9783319684383 010 $a9783319684390 (ebook) 024 7 $a10.1007/978-3-319-68439-0 035 $a(DE-He213)978-3-319-68439-0 035 $a(CKB)4100000001381584 035 $a(MiAaPQ)EBC6314446 035 $a(MiAaPQ)EBC5591722 035 $a(Au-PeEL)EBL5591722 035 $a(OCoLC)1015676520 035 $a(PPN)222228180 035 $a(EXLCZ)994100000001381584 100 $a20171208d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Gauge Theory$b[electronic resource] $eWith Applications to the Standard Model of Particle Physics /$fby Mark J.D. Hamilton 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVIII, 658 p. 40 illus.) 225 1 $aUniversitext,$x0172-5939 327 $aPart 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. 330 $aThe Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix. 410 0$aUniversitext,$x0172-5939 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aElementary particles (Physics) 606 $aQuantum field theory 606 $aPhysics 606 $aTopological groups 606 $aLie groups 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aElementary particles (Physics). 615 0$aQuantum field theory. 615 0$aPhysics. 615 0$aTopological groups. 615 0$aLie groups. 615 14$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aElementary Particles, Quantum Field Theory. 615 24$aMathematical Methods in Physics. 615 24$aTopological Groups, Lie Groups. 676 $a539.72 700 $aHamilton$b Mark J.D$4aut$4http://id.loc.gov/vocabulary/relators/aut$0959448 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910254294903321 996 $aMathematical Gauge Theory$92174094 997 $aUNINA