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书名: | 物理学家用的张量和群论导论 |
作者: | [美]N.杰夫基 |
出版社: | 世界图书出版有限公司 |
出版日期: | 2013-09-01 |
版次: | 1 |
ISBN: | 9787510070266 |
市场价: | 49.0 |
Part I Linear Algebra and TensorsI A Quicklntroduction to Tensors2 VectorSpaces2.1 Definition and Examples2.2 Span,Linearlndependence,and Bases2.3 Components2.4 LinearOperators2.5 DuaISpaces2.6 Non-degenerate Hermitian Forms2.7 Non-degenerate Hermitian Forms and Dual Spaces2.8 Problems3 Tensors3.1 Definition and Examples3.2 ChangeofBasis3.3 Active and Passive Transformations3.4 The Tensor Product-Definition and Properties3.5 Tensor Products of V and V*3.6 Applications ofthe Tensor Product in Classical Physics3.7 Applications of the Tensor Product in Quantum Physics3.8 Symmetric Tensors3.9 Antisymmetric Tensors3.10 ProblemsPartll GroupTheory4 Groups, Lie Groups,and Lie Algebras4.1 Groups-Definition and Examples4.2 The Groups ofClassical and Quantum Physics4.3 Homomorphismandlsomorphism4.4 From Lie Groups to Lie Algebras4.5 Lie Algebras-Definition,Properties,and Examples4.6 The Lie Algebras ofClassical and Quantum Physics4.7 AbstractLieAlgebras4.8 Homomorphism andlsomorphism Revisited4.9 Problems5 Basic Representation Theory5.1 Representations: Definitions and Basic Examples5.2 FurtherExamples5.3 TensorProduet Representations5.4 Symmetric and Antisymmetric Tensor Product Representations5.5 Equivalence ofRepresentations 5.6 Direct Sums andlrreducibility5.7 Moreonlrreducibility5.8 Thelrreducible Representations ofsu(2),SU(2) and S0(3)5.9 ReaIRepresentations andComplexifications5.10 The Irreducible Representations of st(2, C)nk, SL(2, C) andS0(3,1)o5.11 Irreducibility and the Representations of 0(3, 1) and Its Double Covers5.12 Problems6 The Wigner-Eckart Theorem and Other Applications6.1 Tensor Operators, Spherical Tensors and Representation Operators6.2 Selection Rules and the Wigner-Eckart Theorem6.3 Gamma Matrices and Dirac Bilinears6.4 ProblemsAppendix Complexifications of Real Lie Algebras and the TensorProduct Decomposition ofsl(2,C)rt RepresentationsA.1 Direct Sums and Complexifications ofLie AlgebrasA.2 Representations of Complexified Lie Algebras and the TensorProduct Decomposition ofst(2,C)R RepresentationsReferencesIndex
Thiook is composed of two parts: Part I (Chaps. I through 3) is an introduction to tensors and their physical applications, and Part II (Chaps. 4 through 6) introduces group theory and intertwines it with the earlier material. Both parts are written at the advanced-undergraduate/beginning graduate level, although in the course of' Part II the sophistication level rises somewhat. Though the two parts differ somewhat in flavor,l have aimed in both to fill a (perceived) gap in the literaiure by connecting
the component formalisms prevalent in physics calculations to the abstract but more conceptual formulations found in the math literature. My firm beliefis that we need to see tensors and groups in coordinates to get a sense of how they work, but also need an abstract formulation to understand their essential nature and organize our thi about them.
杰夫基编著的《物理学家用的张量和群论导论》是一部讲述张量和群论的物理学专业的教程,用直观、严谨的方法介绍张量和群论以及其在理论物理和应用数学的重要。本书旨在用一种比较的框架,揭开张量的神秘面纱,使得读者在经典物理和量子物理的背景理解它。将物理计算中的许多流形公式和数学中的抽象的或者更加概念公式的联系起来,对张量和群论的的人来说,这项工作是很欢迎的。
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