Group theory in a nutshell for physicists:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton ; Oxford
Princeton University Press
[2016]
|
| Series: | In a nutshell
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xviii, 613 Seiten Illustrationen, Diagramme |
| ISBN: | 9780691162690 |
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Record in the Search Index
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| adam_text | Titel: Group theory in a nutshell for physicists
Autor: Zee, Anthony
Jahr: 2016
Contents
Preface xi
A Brief Review of Linear Algebra l
Q] Part I: Croups: Discrete or Continuous, Finite or Infinite
1.1 Symmetry and Groups 37
1.2 Finite Groups 55
1.3 Rotations and the Notion of Lie Algebra 70
H[J Part II: Representing Croup Elements by Matrices
11.1 Representation Theory 89
11.2 Schur s Lemma and the Great Orthogonality Theorem 101
11.3 Character Is a Function of Class 114
11.4 Real, Pseudoreal, Complex Representations, and the Number
of Square Roots 136
11.11 Crystals Are Beautiful 146
11.12 Euler s ^-Function, Fermat s Little Theorem, and Wilson s Theorem 150
11.13 Frobenius Groups 154
Part III: Croup Theory in a Quantum World
II I.l Quantum Mechanics and Group Theory: Parity, Bloch s Theorem,
and the Brillouin Zone 161
111.2 Group Theory and Harmonie Motion: Zero Modes 168
111.3 Symmetry in the Laws of Physics: Lagrangian and Hamiltonian 176
Contents
IV
VI
Part IV: Tensor, Covering, and Manifold
IV.l Tensors and Representations of the Rotation Groups SO(N) 185
IV.2 Lie Algebra of SO(3) and Ladder Operators: Creation and Annihilation 203
IV.3 Angular Momentum and Clebsch-Gordan Decomposition 216
IV.4 Tensors and Representations of the Special Unitary Groups SU(N) lll
IV.5 SU(2): Double Covering and the Spinor 244
IV.6 The Electron Spin and Kramer s Degeneracy 255
IV.7 Integration over Continuous Groups, Topology, Coset Manifold,
and SO(4) 261
IV.8 Symplectic Groups and Their Algebras 277
IV.9 From the Lagrangian to Quantum Field Theory: It Is but a Skip
and a Hop 283
IV.il Multiplying Irreducible Representations of Finite Groups:
Return to the Tetrahedral Group 289
IV.i2 Crystal Field Splitting 292
IV.i3 Group Theory and Special Functions 295
IV.i4 Covering the Tetrahedron 299
Part V: Group Theory in the Microscopic World
V.l Isospin and the Discovery of a Vast Internal Space 303
V.2 The Eightfold Way of SU(3) 312
V.3 The Lie Algebra of SU(3) and Its Root Vectors 325
V.4 Group Theory Guides Us into the Microscopic World 337
Part VI: Roots, Weights, and Classification of Lie Algebras
VI.l The Poor Man Finds His Roots 347
VI.2 Roots and Weights for Orthogonal, Unitary, and Symplectic Algebras 350
VI.3 Lie Algebras in General 364
VIA The Killing-Cartan Classification of Lie Algebras 376
VI.5 Dynkin Diagrams 384
VII
Part VII: From Galileo to Majorana
VII.1 Spinor Representations of Orthogonal Algebras 405
VII.2 The Lorentz Group and Relativistic Physics 428
VII.3 SL(2,C) Double Covers SO(3,l): Group Theory Leads Us
to the Weyl Equation 450
VI 1.4 From the Weyl Equation to the Dirac Equation 468
VII.5 Dirac and Majorana Spinors: Antimatter and Pseudoreality 482
VII.il A Hidden SO(4) Algebra in the Hydrogen Atom 491
Contents | ix
VII.i2 The Unexpected Emergence of the Dirac Equation in Condensed
Matter Physics 497
VII.i3 The Even More Unexpected Emergence of the Majorana Equation
in Condensed Matter Physics 501
VIII
IX
Part VIII: The Expanding Universe
VIII.l Contraction and Extension 507
VIII.2 The Conformal Algebra 515
VIII.3 The Expanding Universe from Group Theory 523
Part IX: The Cauged Universe
IX.l The Gauged Universe 531
IX.2 Grand Unification and SU(5) 541
IX.3 From SU(5) to SO(IO) 550
IX.4 The Family Mystery 560
Epilogue 565
Timeline of Some of the People Mentioneä 567
Solutions to Selected Exercises 569
Bibliography 581
Index 583
Collection of Formulas 601
|
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| dewey-full | 512.202453 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.202453 |
| dewey-search | 512.202453 |
| dewey-sort | 3512.202453 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| isbn | 9780691162690 |
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| series2 | In a nutshell |
| spelling | Zee, Anthony 1945- Verfasser (DE-588)111982065 aut Group theory in a nutshell for physicists A. Zee Princeton ; Oxford Princeton University Press [2016] © 2016 xviii, 613 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier In a nutshell Hier auch später erschienene, unveränderte Nachdrucke Mathematische Physik Group theory Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Gruppentheorie (DE-588)4072157-7 s Mathematische Physik (DE-588)4037952-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028948560&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zee, Anthony 1945- Group theory in a nutshell for physicists Mathematische Physik Group theory Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4072157-7 (DE-588)4123623-3 |
| title | Group theory in a nutshell for physicists |
| title_auth | Group theory in a nutshell for physicists |
| title_exact_search | Group theory in a nutshell for physicists |
| title_full | Group theory in a nutshell for physicists A. Zee |
| title_fullStr | Group theory in a nutshell for physicists A. Zee |
| title_full_unstemmed | Group theory in a nutshell for physicists A. Zee |
| title_short | Group theory in a nutshell for physicists |
| title_sort | group theory in a nutshell for physicists |
| topic | Mathematische Physik Group theory Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Mathematische Physik Group theory Mathematical physics Gruppentheorie Lehrbuch |
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