Geometry and Physics [electronic resource] / by Jürgen Jost.
Contributor(s): SpringerLink (Online service)Material type: TextPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: XIV, 217 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783642005411Subject(s): Mathematics | Geometry | Differential geometry | Calculus of variations | Physics | Mathematics | Geometry | Differential Geometry | Calculus of Variations and Optimal Control; Optimization | Theoretical, Mathematical and Computational Physics | Mathematical Methods in PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 516 LOC classification: QA440-699Online resources: Click here to access online
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1.Geometry -- 1.1.Riemannian and Lorentzian manifolds -- 1.2.Bundles and connections -- 1.3.Tensors and spinors -- 1.4.Riemann surfaces and moduli spaces -- 1.5.Supermanifolds -- 2.Physics -- 2.1.Classical and quantum physics -- 2.2.Lagrangians.-2.3.Variational aspects -- 2.4.The sigma model -- 2.5.Functional integrals -- 2.6.Conformal field theory -- 2.7.String theory -- Bibliography -- Index.
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.