04631nam 22008535 450 991036085240332120240709094004.097830303141183-030-31411-110.1007/978-3-030-31411-8(CKB)4100000009844896(DE-He213)978-3-030-31411-8(MiAaPQ)EBC5975561(PPN)26914630X(EXLCZ)99410000000984489620191109d2019 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierGeometric multivector analysis from Grassmann to Dirac /Andreas RosénCham :Springer International Publishing :Imprint: Birkhäuser,[2019].©20191 online resource (XIII, 465 pages, 29 illustrations., 8 illustrations. in color.)Birkhäuser Advanced Texts Basler Lehrbücher,2296-48949783030314101 3-030-31410-3 Prelude: Linear algebra -- Exterior algebra -- Clifford algebra -- Mappings of inner product spaces -- Spinors in inner product spaces -- Interlude: Analysis -- Exterior calculus -- Hodge decompositions -- Hypercomplex analysis -- Dirac equations -- Multivector calculus on manifolds -- Two index theorems.This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions. The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics. The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.Birkhäuser Advanced Texts Basler Lehrbücher,2296-4894Algebras, LinearGlobal analysis (Mathematics)Manifolds (Mathematics)Differential equationsIntegral equationsGeometry, DifferentialLinear AlgebraGlobal Analysis and Analysis on ManifoldsDifferential EquationsIntegral EquationsDifferential GeometryAnàlisi global (Matemàtica)lemacÀlgebra lineallemacGeometria diferenciallemacEquacions diferencialslemacEquacions integralslemacVarietats (Matemàtica)lemacAlgebras, Linear.Global analysis (Mathematics).Manifolds (Mathematics).Differential equations.Integral equations.Geometry, Differential.Linear Algebra.Global Analysis and Analysis on Manifolds.Differential Equations.Integral Equations.Differential Geometry.Anàlisi global (Matemàtica)Àlgebra linealGeometria diferencialEquacions diferencialsEquacions integralsVarietats (Matemàtica)512.5Rosén Andreasauthttp://id.loc.gov/vocabulary/relators/aut781339MiAaPQMiAaPQMiAaPQBOOK9910360852403321Geometric Multivector Analysis1732489UNINA