Linear algebra and group theory for physicists:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1996
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 623 S. |
| ISBN: | 0470220619 8122408702 |
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Record in the Search Index
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| adam_text | IMAGE 1
LINEAR ALGEBRA
AND
IROUP THEORY FOR PHYSICISTS
K.N. SRINIVASA RAO PROFESSOR OF THEORETICAL PHYSICS (RETD) UNIVERSITY OF
MYSORE, MYSORE, INDIA
JOHN WILEY SONS NEW YORK * CHICHESTER * BRISBANE * TORONTO * SINGAPORE
IMAGE 2
CONTENTS
CHAPTER 1 ELEMENTS OF GROUP THEORY -1 1.1 1.2 1.3
1.4 1.5 1.6 1.7 1.8
SET-THEORETIC PRELIMINARIES -1 GROUPS - 2 ALGEBRAIC OPERATIONS IN A
GROUP -13 SOME SUBGROUPS OF A GIVEN GROUP G - 13 COSETS -15 THE CLASS OF
CONJUGATES OF A COMPLEX K-17
THE DIRECT PRODUCT OF TWO GROUPS - 22 HOMOMORPHISM AND ISOMORPHISM - 23
CHAPTER 2 SOME RELATED ALGEBRAIC STRUCTURES - 28
2.1 2.2 2.3 2.4 2.5 2.6
RING - 28 DIVISION RING - 30 FIELD-31 LINEAR VECTOR SPACE - 31 LINEAR
ASSOCIATIVE ALGEBRA: HYPER COMPLEX SYSTEM - 32 LIE-RING AND LIE-ALGEBRA
- 34
CHAPTER 3 LINEAR VECTOR SPACE - 35
3.1 3.2 3.3
3.4 3.5 3:6 3.7 3.8 3.9
3.10 3.11 3.12
3.13 3.14
3.15 3.16 3.17
3.18 3.19 3.20
DEFINITION - 35 LINEAR DEPENDENCE AND INDEPENDENCE OF VECTORS - 36
CHANGE OF BASIS - 44
SUBSPACE - 46 ISOMORPHISM OF VECTOR SPACES - 51 ON THE MATRIX PRODUCT
RULE - 52 THE RANK OF A MATRIX - 54 LINEAR TRANSFORMATIONS - 62
SUM AND PRODUCT OF OPERATORS - 68 EFFECT OF CHANGE OF BASIS - 69 ACTIVE
AND PASSIVE POINTS OF VIEW 74 THE RAENGE AND KERNEL OF A LINEAR
TRANSFORMATION - 72
LINEAR TRANSFORMATION OF R N TO S* - 74 INVARIANT SUBSPACE-EIGENVALUES
AND EIGENVECTORS - 75 CAYLEY-HAMILTON THEOREM - 78 EUCLIDEAN SPACE - 85
THE SCHUR CANONICAL FORM - 92 THE DIRECT PRODUCT OF TWO VECTOR
SPACES-THE KRONECKER PRODUCT SPACE - 97 THE MATRIX EXPONENTIAL - 104
SOME PROPERTIES OF HERMITIAN AND UNITARY MATRICES -111 THE DIRAC BRA-KET
NOTATION -119
IMAGE 3
CHAPTER 4 ELEMENTS OF REPRESENTATION THEORY - 124
4.1 DEFINITION OF A REPRESENTATION -124 4.2 SCHUR LEMMA-131 4.3
REPRESENTATIONS OF THE DIRAC ALGEBRAS CI AND C4- 135
4.4 ELEMENTS OF REPRESENTATIONS OF LINEAR GROUPS -141 4.5 GENERALISED
SCHUR LEMMA -150
CHAPTER 5 REPRESENTATIONS OF FINITE GROUPS - 152
5.1 UNITARITY OF A REPRESENTATION -152 5.2 ORTHOGONALITY RELATIONS-156
A) ORTHOGONALITY RELATIONS FOR CHARACTERS -160 B) FROBENIUS CRITERION
FOR IRREDUCIBILITY -161
C) THE REGULAER REPRESENTATION -162 5.3 IRREPS OF SOME FINITE GROUPS -
174
CHAPTER 6 REPRESENTATIONS OF LINEAR ASSOCIATIVE ALGEBRAS - 183
6.1 SIMPLE AND SEMI-SIMPLE ALGEBRAS -183 6.2 OPERATOR HOMOMORPHISM -186
6.3 THE FUNDAMENTAL THEOREM OF SEMI-SIMPLE ALGEBRAS -187 6.4
DECOMPOSITION OF Q INTO TWO-SIDED IDEALS -195
WEDDERBURN S THEOREM - 203 6.5 IDEAL RESOLUTION AND IRREPS OF THE DIRAC
AND KEMMER ALGEBRAS - 209
THE DIRECT PRODUCT OF ALGEBRAS - 234
CHAPTER 7 REPRESENTATIONS OF THE SYMMETRIE GROUP - 239
7.1 THE CHARACTERISTIC OF A PERMUTATION - 239 7.2 THE NUMBER OF ELEMENTS
IN A CLASS - 241 7.3 THE YOUNG TABLEAUX - 242
7.4 LEMMAS FOR THE TABLEAUX - 248 7.5 YOUNG S THEOREM - 252 7.6 THE
IRREDUCIBLE REPRESENTATIONS : THE STANDARD TABLEAUX - 257 7.7
RECIPROCITY BETWEEN THE IRREPS OF GL(N,C) AND SF- 265
CHAPTER 8 ROTATION GROUP AND ITS REPRESENTATIONS - 286
8.1 ROTATION MATRIX IN TERMS OF ITS AXIS AND ANGLE - 286 8.2 THE ANGLE
AND AXIS OF AN ARBITARY PROPER ORTHOGONAL MATRIX - 291 8.3 THE
EIGNVALUES OF A ROTATION MATRIX - 292 8.4 THE CANONICAL FORM OF A
ROTATION MATRIX - 293 8.5 THE EULER RESOLUTION OF A ROTATION - 297
THE EULER-BRAUER RESOLUTION - 303 8.6 QUATERNIONS AND ROTATIONS - 305
8.7 STEREOGRAPHIC PROJEETION AND THE SU(2) REPRESENTATION - 313 8.8
INVARIANT INTEGRAUEON - 315
8.9 IRREPS OF THE ALGEBRA SO(3) - 318 8.10 EXPONENTIATION OF THE
INFINITESIMAL OPERATORS - 329 8.11 THE CHARACTER FORMULA - 337
IMAGE 4
8.12 THE /V REPRESENTATION THROUGH SU(2) - 338
8.13 ORTHOGONALITY AND COMPLETENESS OF THE D-FUNCTIONS - 344
8.14 ADDITIONAL PROPERTIES OF THE D 1 IRREPS - 346 8.15 REPRESENTATION
IN FUNCTION SPACE : IRREDUCIBLE TEUSORS - 353 8.16 DIFFERENTIAL
OPERATORS FOR THE INFINITESIMAL TRANSFORMATIONS SPHERICAL FUNCTIONS -
358 8.17 KRONECKER PRODUCT REPRESENTATION :
CLEBSCH - GORDAN THEOREM - 363 8.18 CLEBSCH - GORDAN CO-EFFICIENTS - 369
8.19 THE WIGNER - ECKART THEOREM - 375 APPENDIX
WIGNER S DERIVATION OF THE C-G COEFFICIENTS - 380
CHAPTER 9 THE CRYSTALLOGRAPHIC POINT GROUPS - 387
9.1 PRELIMINARIES - 387 9.2 FINITE-DIMENSIONAL SUBGROUPS OF SO(3) - 389
9.3 THE CRYSTALLOGRAPHIC POINT GROUPS (FIRST KIND) - 404 9.4 THE
CRYSTALLOGRAPHIC POINT GROUPS OF THE SECOND KIND - 406 9.5 THE CHARACTER
TABLES OF THE POINT GROUPS - 417
CHAPTER 10 THE LORENTZ GROUP AND ITS REPRESENTATIONS - 425
10.1 THE LORENTZ TRANSFORMATION - 425 10.2 MINKOWSKI SPACE - 431
ORTHOGONALITY PROPERTIES OF FOUR-VECTORS - 432 PLANES IN M PASSING
THROUGH THE.ORIGIN AND THEIR CLASSIFICATION - 435
10.3 THE LORENTZ GROUP - 438 THE FOUR PIECES OF T7- 440 SUBGROUPS OF 77-
442
10.4 EIGENVALUES AND EIGENVECTORS OF AN OPLT - 446 10.5 PLANAR
TRANSFORMATIONS - 454 10.6 CANONICAL FORMS OF PLANAR OPLT S - 468 10.7
THE CANONICAL FORM OF AN ARBITRARY NON-NULL OPLT - 473 10.8 SYNGE S
PHYSICAL INTERPRETATION OF NULL AND NON-NULL OPLT S - 480
10.9 OPLT AS A POLYNOMIAL IN THE ILT - 481 10.10 DETERMINATION OF THE
BLADES OF A SCREW-LIKE OPLT - 484 10.11 PLANAR RESOLUTIONS OF AN OPLT -
491 I) OPLT AS A COMMUTING PRODUCT OF TWO ORTHOGONAL PLANAR OPLT S -
491
II) OPLT AS A PRODUCT OF A ROTATION AND A BOOST - 494 III) OPLT AS A
PRODUCT OF TWO INVOLUTIONS - 499 IV) THE EULER RESOLUTION OF AN OPLT -
500 V) THE EULER - BRAUER RESOLUTION OF AN OPLT - 504 10.12 COMPLEX
LIE-CARTAN PARAMETERS OF SO(3,L) - 508 10.13 QUATERNIONS AND OPLT S-516
THE PRODUCT OF TWO BOOSTS; WIGNER ROTATION - 524 THE THOMAS PRECESSION -
525
IMAGE 5
10.14 THE SL(2,C) REPRESENTATION OF SO(3,L) - 530
10.15 SPINORS-535 10.16 THE SO(3,C) REPRESENTATION OF SO(3,L) - 543
10.17 THE FINITE DIMENSIONAL IRREPS OF SO(3,L) - 552 EXPONENTIATION OF
THE INFINITESIMAL OPERATORS - 567
THE D J IRREPS THROUGH SL(2,C) - 571
SPECIAL PROPERTIES OF THE D IRREPS - 573 THE CLEBRSCH-GORDAN THEOREM -
575 THE CHARACTER FORMULA - 576 10.18 IRREPS OF SO(3,L) IN GENERAL - THE
GELFAND-NAIMARK BASIS - 578
SPECIAL PROPERTIES OF THE D(J 0 , C) IRREPS - 586 REALITY CLASSIFICATION
OF THE D{J 0 , C) IRREPS - 598
CHAPTER 11 INTRODUCTION TO THE CLASSIFICATION OF LIE-GROUPS-DYNKIN
DIAGRAMS - 604
11.1 PRELIMINARIES - 604 11.2 COMPLEX EXTENSION OF A REAL LIE-ALGEBRA -
605 11.3 SIMPLE AND SEMI-SIMPLE LIE-ALGEBRAS - 605 11.4 CARTAN S
CRITERION FOR A LIE-ALGEBRA TO BE SEMI SIMPLE - 606
11.5 THE ADJOINT REPRESENTATION - 609 11.6 CLASSIFICATION OF
LIE-GROUPS-DYNKIN DIAGRAMS - 610 DYNKIN DIAGRAMS - 613
INDEX 620-623
|
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| dewey-raw | 512.5 |
| dewey-search | 512.5 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| spelling | Srinivasa Rao, K. Verfasser aut Linear algebra and group theory for physicists K. N. Srinivasa Rao 1. publ. New York [u.a.] Wiley 1996 623 S. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik Algebras, Linear Group theory Mathematical physics Physiker (DE-588)4045968-8 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s Physiker (DE-588)4045968-8 s DE-604 Gruppentheorie (DE-588)4072157-7 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007834934&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Srinivasa Rao, K. Linear algebra and group theory for physicists Mathematische Physik Algebras, Linear Group theory Mathematical physics Physiker (DE-588)4045968-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4045968-8 (DE-588)4072157-7 (DE-588)4035811-2 |
| title | Linear algebra and group theory for physicists |
| title_auth | Linear algebra and group theory for physicists |
| title_exact_search | Linear algebra and group theory for physicists |
| title_full | Linear algebra and group theory for physicists K. N. Srinivasa Rao |
| title_fullStr | Linear algebra and group theory for physicists K. N. Srinivasa Rao |
| title_full_unstemmed | Linear algebra and group theory for physicists K. N. Srinivasa Rao |
| title_short | Linear algebra and group theory for physicists |
| title_sort | linear algebra and group theory for physicists |
| topic | Mathematische Physik Algebras, Linear Group theory Mathematical physics Physiker (DE-588)4045968-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Mathematische Physik Algebras, Linear Group theory Mathematical physics Physiker Gruppentheorie Lineare Algebra |
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