03784nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118040002500153050001600178050001900194072001700213072002300230072001600253072001600269082001500285100008100300245014200381264007500523300004600598336002600644337002600670338003600696347002400732490002900756505061000785520111601395650003502511650002002546650002602566650002402592650012702616650011902743650010802862650010702970710003403077773002003111776003603131776003603167830002903203856004603232978-3-319-68439-0DE-He21320181204134423.0cr nn 008mamaa171208s2017 gw | s |||| 0|eng d a97833196843907 a10.1007/978-3-319-68439-02doi aISI Library, Kolkata 4aQA613-613.8 4aQA613.6-613.66 7aPBMS2bicssc 7aMAT0380002bisacsh 7aPBMS2thema 7aPBPH2thema04a514.342231 aHamilton, Mark J.D.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aMathematical Gauge Theoryh[electronic resource] :bWith Applications to the Standard Model of Particle Physics /cby Mark J.D. Hamilton. 1aCham :bSpringer International Publishing :bImprint: Springer,c2017. aXVIII, 658 p. 40 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext,x0172-59390 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. 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. 0aCell aggregationxMathematics. 0aQuantum theory. 0aMathematical physics. 0aTopological Groups.14aManifolds and Cell Complexes (incl. Diff.Topology).0http://scigraph.springernature.com/things/product-market-codes/M2802724aElementary Particles, Quantum Field Theory.0http://scigraph.springernature.com/things/product-market-codes/P2302924aMathematical Methods in Physics.0http://scigraph.springernature.com/things/product-market-codes/P1901324aTopological Groups, Lie Groups.0http://scigraph.springernature.com/things/product-market-codes/M111322 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978331968438308iPrinted edition:z9783319684406 0aUniversitext,x0172-593940uhttps://doi.org/10.1007/978-3-319-68439-0