Group representation for quantum theory. ([2016])

• Record Type: Book
• Further Information: Note: Masahito Hayashi.
• Authors: Hayashi, Masahito
• Contents: Preface; Preface to the Japanese Version; Contents; About the Author; Symbols; 1 Mathematical Foundation for Quantum System; 1.1 System, State, and Measurement; 1.2 Composite System; 1.2.1 Tensor Product System; 1.2.2 Entangled State; 1.3 Many-Body System; 1.4 Hamiltonian; 1.4.1 Dynamics and Hamiltonian; 1.4.2 Simultaneous Diagonalization; 1.4.3 Relation to Representation; 1.5 Relation to Symmetry; 1.6 Remark for Unbounded Case*; 2 Group Representation Theory; 2.1 Group and Homogeneous Space; 2.1.1 Group; 2.1.2 Homogeneous Space; 2.2 Extension of Group; 2.2.1 General Case. 2.2.2 Central Extension of a Commutative Group2.2.3 Examples for Central Extensions; 2.3 Representation and Projective Representation; 2.3.1 Definitions of Representation and Projective Representation; 2.3.2 Schur's Lemma; 2.3.3 Representations of Direct Product Group; 2.4 Projective Representation and Extension of Group; 2.4.1 Factor System of Projective Representation; 2.4.2 Irreducibility and Projective Representation; 2.4.3 Extension by U(1) ; 2.5 Semi Direct Product and Its Representation; 2.5.1 From HK to K and H; 2.5.2 From K and H to HK* 2.6 Real Representation and Complex Conjugate Representation2.6.1 Real Linear Space and Its Complexification; 2.6.2 Real Representation; 2.6.3 Complex Conjugate Representation; 2.7 Representation on Composite System; 2.8 Fourier Transform for Finite Group; 2.8.1 Discrete Fourier Transform; 2.8.2 Character and Orthogonality; 2.8.3 Fourier Transform; 2.9 Representation of Permutation Group and Young Diagram; 2.9.1 Young Diagram and Young Tableau; 2.9.2 Permutation Group and Young Diagram; 2.9.3 Plancherel Measure; 3 Foundation of Representation Theory of Lie Group and Lie Algebra. 3.1 Lie Group3.1.1 Basic Examples; 3.1.2 Symmetry in Analytical Mechanics; 3.1.3 Complex Lie Group; 3.1.4 Other Examples of Real Lie Groups; 3.2 Lie Algebra; 3.3 Relation Between Lie Group and Lie Algebra I; 3.3.1 Infinitesimal Transformation and Lie Algebra; 3.3.2 Examples; 3.3.3 Central Extension of Real Lie Algebra; 3.4 Representation of Lie Algebra; 3.4.1 Representation of Real Lie Algebra; 3.4.2 Real Representation; 3.4.3 Representation of Complex Lie Algebra; 3.4.4 Adjoint Representation; 3.4.5 Projective Representation; 3.4.6 Semi Direct Product Lie Algebra and Representation. 3.5 Killing Form and Compactness3.5.1 Killing Form; 3.5.2 Compactness of Real Lie Algebra mathfrakg; 3.5.3 Casimir Operator; 3.6 Relation Between Lie Group and Lie Algebra II; 3.6.1 Universal Covering Group; 3.6.2 Relation to Representation; 3.6.3 Projective Representation; 3.6.4 Representation for Complex Lie Groups; 3.7 Invariant Measures on Group and Homogeneous Space; 3.8 Fourier Transform on Lie Group; 3.8.1 Commutative Case; 3.8.2 Non-commutative Case; 4 Representations of Typical Lie Groups and Typical Lie Algebras; 4.1 SL(2, mathbbC) and Its Subgroup.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2016
• Copyright Date: 2017
• Extent: 1 online resource (XXVIII, 338 pages 54 illustrations)
• Subjects: 512/.22; 530; Physics; Representations of groups; Quantum theory; MATHEMATICS -- Algebra -- Intermediate; Quantum theory; Representations of groups; Mathematics -- Algebra -- Abstract; Computers -- Information Technology; Science -- Quantum Theory; Science -- Mathematical Physics; Groups & group theory; Quantum physics (quantum mechanics & quantum field theory); Mathematical theory of computation; Mathematical physics; Group theory; Electronic books
• Languages: English
• ISBNs: 9783319449067; 3319449060
• Related ISBNs: 9783319449043; 3319449044
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed December 7, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.