Mathematical Gauge Theory
Springer International Publishing (Verlag)
978-3-319-68438-3 (ISBN)
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.Mark Hamilton has worked as a lecturer and interim professor at the University of Stuttgart and the Ludwig-Maximilian University of Munich. His research focus lies on geometric topology and mathematical physics, in particular, the differential topology of 4-manifolds and Seiberg-Witten theory.
Part 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.
"Assuming an introductory course on differential geometry and some basic knowledge of special relativity, both of which are summarized in the appendices, the book expounds the mathematical background behind the well-established standard model of modern particle and high energy physics... I believe that the book will be a standard textbook on the standard model for mathematics-oriented students." (Hirokazu Nishimura, zbMATH 1390.81005)
“Assuming an introductory course on differential geometry and some basic knowledge of special relativity, both of which are summarized in the appendices, the book expounds the mathematical background behind the well-established standard model of modern particle and high energy physics… I believe that the book will be a standard textbook on the standard model for mathematics-oriented students.” (Hirokazu Nishimura, zbMATH 1390.81005)
| Erscheinungsdatum | 09.01.2018 |
|---|---|
| Reihe/Serie | Universitext |
| Zusatzinfo | XVIII, 658 p. 40 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1006 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | 81T13, 81R40, 81V19, 81V05, 81V10, 81V15 • analytic geometry • Analytic topology • connections and curvature • Electroweak interaction • Elementary Particles, Quantum Field Theory • Gauge Theory • gauge theory and Lagrangians • gauge theory mathematics • gauge theory of the Standard Model • Grand Unified Theory • Groups & group theory • Groups & group theory • Higgs Boson Standard Model • Higss boson • Lagrangian • Manifolds and Cell Complexes (incl. Diff.Topology) • Mathematical methods in physics • Mathematical Physics • Mathematics • mathematics and statistics • MSC (2010) 55R10, 53C05, 22E70, 15A66, 53C27, 57S1 • MSC (2010) 55R10, 53C05, 22E70, 15A66, 53C27, 57S15, 22E60 • principal bundle • quantum chromodynamics qcd theory • Quantum physics (quantum mechanics & quantum field • Quantum physics (quantum mechanics & quantum field • Spinor • Spontaneous Symmetry Breaking • standard model of elementary particle physics • Topological Groups, Lie Groups • vector bundle |
| ISBN-10 | 3-319-68438-8 / 3319684388 |
| ISBN-13 | 978-3-319-68438-3 / 9783319684383 |
| Zustand | Neuware |
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