Lectures on advanced mathematical methods for physicists:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific [u.a.]
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | VIII, 278 S. graph. Darst. |
| ISBN: | 9789814299732 9814299731 |
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MARC
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Record in the Search Index
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| adam_text | IMAGE 1
LECTURES ON ADVANCED
MATHEMATICAL METHODS
FOR PHYSICISTS
TATA INSTITUTE OF FUNDAMENTAL RESEARCH, INDIA
FORMERLY OF INDIAN INSTITUTE OF SCIENCE, INDIA
TECHNJSCHE
INFORMATIONSB13LIOTHEK
UNIVERSITATSBIBLIOTHEK HANNOVER ^^_I
*
I
1.1-
DLHHINDUSTAN U UL1 U BOOKAGENCY
P WORLD SCIENTIFIC
NEW JERSEY LONDON * SINGAPORE . BEIJING . SHANGHAI * HONG KONG * TAIPEI
* CHENNAI
SUNIL MUKHI
N MUKUNDA
IMAGE 2
CONTENTS
PART I: TOPOLOGY AND DIFFERENTIAL GEOMETRY 1
INTRODUCTION TO PART I 3
1
TOPOLOGY 5
1.1 PRELIMINARIES 5
1.2 TOPOLOGICAL SPACES 6
1.3 METRIC SPACES 9
1.4 BASIS FOR A TOPOLOGY 11
1.5 CLOSURE 12
1.6 CONNECTED AND COMPACT SPACES 13
1.7 CONTINUOUS FUNCTIONS 15
1.8 HORNEOMORPLIISMS 17
1.9 SEPARABILITY 18
2 HOMOTOPY 21
2.1 LOOPS AND HOMOTOPIES 21
2.2 THE FUNDAMENTAL GROUP 25
2.3 HOMOTOPY TYPE AND CONTRACTIBILITY 28
2.4 HIGHER HOMOTOPY GROUPS 34
3
DIFFERENTIABLE MANIFOLDS I 41
3.1 THE DEFINITION OF A MANIFOLD 41
3.2 DIFFERENTIATION OF FUNCTIONS 47
3.3 ORIENTABILITY 48
3.4 CALCULUS ON MANIFOLDS: VECTOR AND TENSOR FIELDS 50
3.5 CALCULUS ON MANIFOLDS: DIFFERENTIAL FORMS 55
3.6 PROPERTIES OF DIFFERENTIAL FORMS 59
3.7 MORE ABOUT VECTORS AND FORMS 62
4 DIFFERENTIABLE MANIFOLDS II 65
4.1 RIEMANNIAN GEOMETRY 65
IMAGE 3
CONTENTS
4.2 FRAMES 67
4.3 CONNECTIONS, CURVATURE AND TORSION 69
4.4 THE VOLUME FORM 74
4.5 ISOMETRY 76
4.6 INTEGRATION OF DIFFERENTIAL FORMS 77
4.7 STOKES THEOREM 80
4.8 THE LAPLACIAN ON FORMS 83
5 HOMOLOGY AND COHOMOLOGY 87
5.1 SIMPLICIAL HOMOLOGY 87
5.2 DE RHAM COHOMOLOGY 100
5.3 HARMONIC FORMS AND DE RHAM COHOMOLOGY 103
6 FIBRE BUNDLES 105
6.1 THE CONCEPT OF A FIBRE BUNDLE 105
6.2 TANGENT AND COTANGENT BUNDLES ILL
6.3 VECTOR BUNDLES AND PRINCIPAL BUNDLES 112
BIBLIOGRAPHY FOR PART I 117
PART II: GROUP THEORY AND STRUCTURE AND REPRESENTATIONS OF COM PACT
SIMPLE LIE GROUPS AND ALGEBRAS 119
INTRODUCTION TO PART II 121
7 REVIEW OF GROUPS AND RELATED STRUCTURES 123
7.1 DEFINITION OF A GROUP 123
7.2 CONJUGATE ELEMENTS, EQUIVALENCE CLASSES 124
7.3 SUBGROUPS AND COSETS 124
7.4 INVARIANT (NORMAL) SUBGROUPS, THE FACTOR GROUP 125
7.5 ABELIAN GROUPS, COMMUTATOR SUBGROUP 126
7.6 SOLVABLE, NILPOTENT, SEMISIMPLE AND SIMPLE GROUPS 127
7.7 RELATIONSHIPS AMONG GROUPS 129
7.8 WAYS TO COMBINE GROUPS - DIRECT AND SEMIDIRECT PRODUCTS . . 131 7.9
TOPOLOGICAL GROUPS, LIE GROUPS, COMPACT LIE GROUPS 132
8 REVIEW OF GROUP REPRESENTATIONS 135
8.1 DEFINITION OF A REPRESENTATION 135
8.2 INVARIANT SUBSPACES, REDUCIBILITY, DECOMPOSABILITY 136 8.3
EQUIVALENCE OF REPRESENTATIONS, SCHUR S LEMMA 138
8.4 UNITARY AND ORTHOGONAL REPRESENTATIONS 139
8.5 CONTRAGREDIENT, ADJOINT AND COMPLEX CONJUGATE REPRESENTATIONS 140
8.6 DIRECT PRODUCTS OF GROUP REPRESENTATIONS 144
IMAGE 4
CONTENTS VII
9 LIE GROUPS AND LIE ALGEBRAS 147
9.1 LOCAL COORDINATES IN A LIE GROUP 147
9.2 ANALYSIS OF ASSOCIATIVITY 148
9.3 ONE-PARAMETER SUBGROUPS AND CANONICAL COORDINATES 151 9.4
INTEGRABILITY CONDITIONS AND STRUCTURE CONSTANTS 155
9.5 DEFINITION OF A (REAL) LIE ALGEBRA: LIE ALGEBRA OF A GIVEN LIE GROUP
157 9.6 LOCAL RECONSTRUCTION OF LIE GROUP FROM LIE ALGEBRA 158
9.7 COMMENTS ON THE G G RELATIONSHIP 160
9.8 VARIOUS KINDS OF AND OPERATIONS WITH LIE ALGEBRAS 161
10 LINEAR REPRESENTATIONS OF LIE ALGEBRAS 165
11 COMPLEXIFICATION AND CLASSIFICATION OF LIE ALGEBRAS 171 11.1
COMPLEXIFICATION OF A REAL LIE ALGEBRA 171
11.2 SOLVABILITY, LEVI S THEOREM, AND CARTAN S ANALYSIS OF COMPLEX
(SEMI) SIMPLE LIE ALGEBRAS 173
11.3 THE REAL COMPACT SIMPLE LIE ALGEBRAS 180
12 GEOMETRY OF ROOTS FOR COMPACT SIMPLE LIE ALGEBRAS 183
13 POSITIVE ROOTS, SIMPLE ROOTS, DYNKIN DIAGRAMS 189 13.1 POSITIVE ROOTS
189
13.2 SIMPLE ROOTS AND THEIR PROPERTIES 189
13.3 DYNKIN DIAGRAMS 194
14 LIE ALGEBRAS AND DYNKIN DIAGRAMS FOR SO(2/), SO(2/+L), USP(2Z), SU(I
+ L) 197
14.1 THE SO(2Z) FAMILY - DT OF CARTAN 197
14.2 THE SO(2Z + 1) FAMILY - BT OF CARTAN 201
14.3 THE USP(2/) FAMILY - D OF CARTAN 203
14.4 THE SU(J + 1) FAMILY - A,, OF CARTAN 207
14.5 COINCIDENCES FOR LOW DIMENSIONS AND CONNECTEDNESS 212
15 COMPLETE CLASSIFICATION OF ALL CSLA SIMPLE ROOT SYSTEMS 215 15.1
SERIES OF LEMMAS 216
15.2 THE ALLOWED GRAPHS T 220
15.3 THE EXCEPTIONAL GROUPS 224
16 REPRESENTATIONS OF COMPACT SIMPLE LIE ALGEBRAS 227 16.1 WEIGHTS AND
MULTIPLICITIES . . 227
16.2 ACTIONS OF EA AND SU(2) FT - THE WEYL GROUP 228
16.3 DOMINANT WEIGHTS, HIGHEST WEIGHT OF A UIR 230
16.4 FUNDAMENTAL UIR S, SURVEY OF ALL UIR S 233
16.5 FUNDAMENTAL UIR S FOR AU BI,Q,DI 234
IMAGE 5
VIII CONTENTS
16.6 THE ELEMENTARY UIR S 240
16.7 STRUCTURE OF STATES WITHIN A UIR 241
17 SPINOR REPRESENTATIONS FOR REAL ORTHOGONAL GROUPS 245 17.1 THE DIRAC
ALGEBRA IN EVEN DIMENSIONS 246
17.2 GENERATORS, WEIGHTS AND REDUCIBILITY OF U(S) - THE SPINOR UIR S OF
DI 248
17.3 CONJUGATION PROPERTIES OF SPINOR UIR S OF A 250
17.4 REMARKS ON ANTISYMMETRIC TENSORS UNDER DI = SO(21) 252 17.5 THE
SPINOR UIR S OF BT = SO(2L + 1) 257
17.6 ANTISYMMETRIC TENSORS UNDER S; = SO(2/ +1) 260
18 SPINOR REPRESENTATIONS FOR REAL PSEUDO ORTHOGONAL GROUPS 261 18.1
DEFINITION OF SO(Q,P) AND NOTATIONAL PATTERS 261
18.2 SPINOR REPRESENTATIONS S(A) OF SO(P, Q) FOR P + Q = 21 262
18.3 REPRESENTATIONS RELATED TO S(A) 264
18.4 BEHAVIOUR OF THE IRREDUCIBLE SPINOR REPRESENTATIONS S(A) . . . 265
18.5 SPINOR REPRESENTATIONS OF SO(P, Q) FOR P + Q = 21 + 1 266
18.6 DIRAC, WEYL AND MAJORANA SPINORS FOR SO(P, Q) 267
BIBLIOGRAPHY FOR PART II 273
INDEX 275
|
| any_adam_object | 1 |
| author | Mukhi, Sunil 1956- Mukunda, Narasimhaiengar 1939- |
| author_GND | (DE-588)142224014 (DE-588)110436180 |
| author_facet | Mukhi, Sunil 1956- Mukunda, Narasimhaiengar 1939- |
| author_role | aut aut |
| author_sort | Mukhi, Sunil 1956- |
| author_variant | s m sm n m nm |
| building | Verbundindex |
| bvnumber | BV036651194 |
| classification_tum | PHY 014f PHY 011f PHY 012f |
| ctrlnum | (OCoLC)705778535 (DE-599)OBVAC08089522 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV036651194 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:57Z |
| institution | BVB |
| isbn | 9789814299732 9814299731 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020570702 |
| oclc_num | 705778535 |
| open_access_boolean | 1 |
| owner | DE-91G DE-BY-TUM DE-83 DE-19 DE-BY-UBM |
| owner_facet | DE-91G DE-BY-TUM DE-83 DE-19 DE-BY-UBM |
| physical | VIII, 278 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific [u.a.] |
| record_format | marc |
| spelling | Mukhi, Sunil 1956- Verfasser (DE-588)142224014 aut Lectures on advanced mathematical methods for physicists Sunil Mukhi & N. Mukunda Singapore [u.a.] World Scientific [u.a.] 2010 VIII, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s Differentialgeometrie (DE-588)4012248-7 s Mathematische Physik (DE-588)4037952-8 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Lie-Algebra (DE-588)4130355-6 s Mukunda, Narasimhaiengar 1939- Verfasser (DE-588)110436180 aut DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/625841735.pdf kostenfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020570702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mukhi, Sunil 1956- Mukunda, Narasimhaiengar 1939- Lectures on advanced mathematical methods for physicists Lie-Algebra (DE-588)4130355-6 gnd Mathematische Physik (DE-588)4037952-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4037952-8 (DE-588)4012248-7 (DE-588)4035695-4 (DE-588)4060425-1 |
| title | Lectures on advanced mathematical methods for physicists |
| title_auth | Lectures on advanced mathematical methods for physicists |
| title_exact_search | Lectures on advanced mathematical methods for physicists |
| title_full | Lectures on advanced mathematical methods for physicists Sunil Mukhi & N. Mukunda |
| title_fullStr | Lectures on advanced mathematical methods for physicists Sunil Mukhi & N. Mukunda |
| title_full_unstemmed | Lectures on advanced mathematical methods for physicists Sunil Mukhi & N. Mukunda |
| title_short | Lectures on advanced mathematical methods for physicists |
| title_sort | lectures on advanced mathematical methods for physicists |
| topic | Lie-Algebra (DE-588)4130355-6 gnd Mathematische Physik (DE-588)4037952-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd Lie-Gruppe (DE-588)4035695-4 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Lie-Algebra Mathematische Physik Differentialgeometrie Lie-Gruppe Topologie |
| url | http://www.gbv.de/dms/tib-ub-hannover/625841735.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020570702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mukhisunil lecturesonadvancedmathematicalmethodsforphysicists AT mukundanarasimhaiengar lecturesonadvancedmathematicalmethodsforphysicists |
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