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An Introduction to Tensors and Group Theory for Physicists / by Nadir Jeevanjee
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: New York, NY [u.a.] : Springer, 2011Edition: 1Description: Online-Ressource (XVI, 242p. 12 illus, digital)ISBN:- 9780817647155
- 512.202453
- 530.15
- QA401-425 QC19.2-20.85
- QC20.7.C28
Contents:
Summary: Part I Linear Algebra and Tensors -- A Quick Introduction to Tensors.- Vector Spaces -- Tensors -- Part II Group Theory -- Groups, Lie Groups, and Lie Algebras.- Basic Representation Theory -- The Winger-Echart Theorem and Other Applications -- Appendix Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R.- References -- Index.Summary: An Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will be a welcome addition to the literature on tensors and group theory. Part I of the text begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to classical and quantum physics through the use of tensor products. Part II introduces abstract groups along with matrix Lie groups and Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Exercises and examples are provided throughout for good practice in applying the presented definitions and techniques. Advanced undergraduate and graduate students in physics and applied mathematics will find clarity and insight into the subject in this textbook.PPN: PPN: 165101938XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""An Introduction to Tensors and Group Theory for Physicists""; ""Preface""; ""Acknowledgements""; ""Contents""; ""Notation""; ""Part I: Linear Algebra and Tensors""; ""Chapter 1: A Quick Introduction to Tensors""; ""Chapter 2: Vector Spaces""; ""2.1 Definition and Examples""; ""2.2 Span, Linear Independence, and Bases""; ""2.3 Components""; ""2.4 Linear Operators""; ""2.5 Dual Spaces""; ""2.6 Non-degenerate Hermitian Forms""; ""2.7 Non-degenerate Hermitian Forms and Dual Spaces""; ""2.8 Problems""; ""Chapter 3: Tensors""; ""3.1 Definition and Examples""; ""3.2 Change of Basis""
""3.3 Active and Passive Transformations""""3.4 The Tensor Product-Definition and Properties""; ""3.5 Tensor Products of V and V*""; ""3.6 Applications of the Tensor Product in Classical Physics""; ""3.7 Applications of the Tensor Product in Quantum Physics""; ""3.8 Symmetric Tensors""; ""3.9 Antisymmetric Tensors""; ""3.10 Problems""; ""Part II: Group Theory""; ""Chapter 4: Groups, Lie Groups, and Lie Algebras""; ""4.1 Groups-Definition and Examples""; ""4.2 The Groups of Classical and Quantum Physics""; ""4.3 Homomorphism and Isomorphism""; ""4.4 From Lie Groups to Lie Algebras""
""4.5 Lie Algebras-Definition, Properties, and Examples""""4.6 The Lie Algebras of Classical and Quantum Physics""; ""4.7 Abstract Lie Algebras""; ""4.8 Homomorphism and Isomorphism Revisited""; ""4.9 Problems""; ""Chapter 5: Basic Representation Theory""; ""5.1 Representations: Definitions and Basic Examples""; ""5.2 Further Examples""; ""5.3 Tensor Product Representations""; ""5.4 Symmetric and Antisymmetric Tensor Product Representations""; ""5.5 Equivalence of Representations""; ""5.6 Direct Sums and Irreducibility""; ""5.7 More on Irreducibility""
""5.8 The Irreducible Representations of su(2), SU(2) and SO(3)""""5.9 Real Representations and Complexifications""; ""5.10 The Irreducible Representations of sl(2,C)R, SL(2,C) and SO(3,1)o""; ""5.11 Irreducibility and the Representations of O(3,1) and Its Double Covers""; ""5.12 Problems""; ""Chapter 6: The Wigner-Eckart Theorem and Other Applications""; ""6.1 Tensor Operators, Spherical Tensors and Representation Operators""; ""6.2 Selection Rules and the Wigner-Eckart Theorem""; ""6.3 Gamma Matrices and Dirac Bilinears""; ""6.4 Problems""
""Appendix : Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R Representations""""A.1 Direct Sums and Complexifications of Lie Algebras""; ""A.2 Representations of Complexified Lie Algebras and the Tensor Product Decomposition of sl(2,C)R Representations""; ""References""; ""Index""
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