| 书目名称 | Geometric Multivector Analysis | | 副标题 | From Grassmann to Di | | 编辑 | Andreas Rosén | | 视频video | | | 概述 | Develops carefully the foundations of calculus of multivector fields and differential forms.Explains advanced material in a self-contained and down-to-earth way, e.g. Clifford algebra, spinors, differ | | 丛书名称 | Birkhäuser Advanced Texts‘ Basler Lehrbücher | | 图书封面 |  | | 描述 | .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 comp | | 出版日期 | Textbook 2019 | | 关键词 | Clifford algebra; exterior algebra; spinors; Hodge decompositions; dirac equations; boundary value proble | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-31411-8 | | isbn_softcover | 978-3-030-31413-2 | | isbn_ebook | 978-3-030-31411-8Series ISSN 1019-6242 Series E-ISSN 2296-4894 | | issn_series | 1019-6242 | | copyright | Springer Nature Switzerland AG 2019 |
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发表于 2025-3-21 16:13:48
