Geometry, topology and physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Bristol <<[u.a.]>>
Institut of Physics Publ.
2003
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate student series in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 573 S. graph. Darst. |
| ISBN: | 0750306068 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804140502269820928 |
|---|---|
| adam_text | GRADUATE STUDENT SERIES IN PHYSICS SERIES EDITOR: PROFESSOR DOUGLAS F
BREWER, MA, DPHIL EMERITUS PROFESSOR OF EXPERIMENTAL PHYSICS, UNIVERSITY
OF SUSSEX GEOMETRY, TOPOLOGY AND PHYSICS SECOND EDITION MIKIO NAKAHARA
DEPARTMENT OF PHYSICS KINKI UNIVERSITY, OSAKA, JAPAN TAYLOR & FRANCIS
TAYLOR & FRANCIS CROUP NEW YORK LONDON CONTENTS PREFACE TO THE FIRST
EDITION XVII PREFACE TO THE SECOND EDITION XIX HOW TO READ THIS BOOK XXI
NOTATION AND CONVENTIONS XXII 1 QUANTUM PHYSICS 1 1.1 ANALYTICAL
MECHANICS 1 1.1.1 NEWTONIAN MECHANICS 1 1.1.2 LAGRANGIAN FORMALISM 2
1.1.3 HAMILTONIAN FORMALISM 5 1.2 CANONICAL QUANTIZATION 9 1.2.1 HILBERT
SPACE, BRAS AND KETS 9 1.2.2 AXIOMS OF CANONICAL QUANTIZATION 10 1.2.3
HEISENBERG EQUATION, HEISENBERG PICTURE AND SCHRODINGER PICTURE 13 1.2.4
WAVEFUNCTION 13 1.2.5 HARMONIC OSCILLATOR 17 1.3 PATH INTEGRAL
QUANTIZATION OF A BOSE PARTICLE 19 1.3.1 PATH INTEGRAL QUANTIZATION 19
1.3.2 IMAGINARY TIME AND PARTITION FUNCTION 26 1.3.3 TIME-ORDERED
PRODUCT AND GENERATING FUNCTIONAL 28 1.4 HARMONIC OSCILLATOR 31 1.4.1
TRANSITION AMPLITUDE 31 1.4.2 PARTITION FUNCTION 35 1.5 PATH INTEGRAL
QUANTIZATION OF A FERMI PARTICLE 38 1.5.1 FERMIONIC HARMONIC OSCILLATOR
^ 39 1.5.2 CALCULUS OF GRASSMANN NUMBERS 40 1.5.3 DIFFERENTIATION 41
1.5.4 INTEGRATION 42 1.5.5 DELTA-FUNCTION 43 1.5.6 GAUSSIAN INTEGRAL 44
1.5.7 FUNCTIONAL DERIVATIVE 45 1.5.8 COMPLEXCONJUGATION 45 1.5.9
COHERENT STATES AND COMPLETENESS RELATION 46 VIII CONTENTS 1.6 1.7 1.8
1.9 1.10 1.5.10 PARTITION FUNCTION OF A TERMIONIC OSCILLATOR
QUANTIZATION OF A SCALAR FIELD 1.6.1 FREE SCALAR FIELD 1.6.2 INTERACTING
SCALAR FIELD QUANTIZATION OF A DIRAC FIELD GAUGE THEORIES 1.8.1 ABELIAN
GAUGE THEORIES 1.8.2 NON-ABELIAN GAUGE THEORIES 1.8.3 HIGGS FIELDS
MAGNETIC MONOPOLES 1.9.1 DIRAC MONOPOLE 1.9.2 THE WU-YANG MONOPOLE 1.9.3
CHARGE QUANTIZATION INSTANTONS 1.10.1 INTRODUCTION 1.10.2 THE
(ANTI-)SELF-DUAL SOLUTION PROBLEMS 2 MATHEMATICAL PRELIMINARIES 2.1 2.2
2.3 2.4 MAPS 2.1.1 DEFINITIONS 2.1.2 EQUIVALENCE RELATION AND
EQUIVALENCE CLASS VECTOR SPACES 2.2.1 VECTORS AND VECTOR SPACES 2.2.2
LINEAR MAPS, IMAGES AND KERNELS 2.2.3 DUAL VECTOR SPACE 2.2.4 INNER
PRODUCT AND ADJOINT 2.2.5 TENSORS TOPOLOGICAL SPACES 2.3.1 DEFINITIONS
2.3.2 CONTINUOUS MAPS 2.3.3 NEIGHBOURHOODS AND HAUSDORFF SPACES 2.3.4
CLOSED SET 2.3.5 COMPACTNESS ** 2.3.6 CONNECTEDNESS HOMEOMORPHISMS AND
TOPOLOGICAL INVARIANTS 2.4.1 HOMEOMORPHISMS 2.4.2 TOPOLOGICAL INVARIANTS
2.4.3 HOMOTOPY TYPE 2.4.4 EULER CHARACTERISTIC: AN EXAMPLE PROBLEMS 47
51 51 54 55 56 56 58 60 60 61 62 62 63 63 64 66 67 67 67 70 75 75 76 77
78 80 81 81 82 82 83 83 85 85 85 86 88 88 91 CONTENTS IX HOMOLOGY GROUPS
93 3.1 ABELIAN GROUPS 93 3.1.1 ELEMENTARY GROUP THEORY 93 3.1.2 FINITELY
GENERATED ABELIAN GROUPS AND FREE ABELIAN GROUPS 96 3.1.3 CYCLIC GROUPS
96 3.2 SIMPLEXES AND SIMPLICIAL COMPLEXES 98 3.2.1 SIMPLEXES 98 3.2.2
SIMPLICIAL COMPLEXES AND POLYHEDRA 99 3.3 HOMOLOGY GROUPS OF SIMPLICIAL
COMPLEXES 100 3.3.1 ORIENTED SIMPLEXES 100 3.3.2 CHAIN GROUP, CYCLE
GROUP AND BOUNDARY GROUP 102 3.3.3 HOMOLOGY GROUPS 106 3.3.4 COMPUTATION
OF H O (K) 110 3.3.5 MORE HOMOLOGY COMPUTATIONS 111 3.4 GENERAL
PROPERTIES OF HOMOLOGY GROUPS 117 3.4.1 CONNECTEDNESS AND HOMOLOGY
GROUPS 117 3.4.2 STRUCTURE OF HOMOLOGY GROUPS 118 3.4.3 BETTI NUMBERS
AND THE EULER-POINCARE THEOREM 118 PROBLEMS * 120 HOMOTOPY GROUPS 121
4.1 FUNDAMENTAL GROUPS 121 4.1.1 BASIC IDEAS 121 4.1.2 PATHS AND LOOPS
122 4.1.3 HOMOTOPY 123 4.1.4 FUNDAMENTAL GROUPS 125 4.2 GENERAL
PROPERTIES OF FUNDAMENTAL GROUPS 127 4.2.1 ARCWISE CONNECTEDNESS AND
FUNDAMENTAL GROUPS 127 4.2.2 HOMOTOPIC INVARIANCE OF FUNDAMENTAL GROUPS
128 4.3 EXAMPLES OF FUNDAMENTAL GROUPS 131 4.3.1 FUNDAMENTAL GROUP OF
TORUS 133 4.4 FUNDAMENTAL GROUPS OF POLYHEDRA 134 4.4.1 FREE GROUPS AND
RELATIONS 134 4.4.2 CALCULATING FUNDAMENTAL GROUPS OF POLYHEDRA 136
4.4.3 RELATIONS BETWEEN H {K) AND TT { K ) 144 4.5 HIGHER HOMOTOPY
GROUPS ._, 145 4.5.1 DEFINITIONS 146 4.6 GENERAL PROPERTIES OF HIGHER
HOMOTOPY GROUPS 148 4.6.1 ABELIAN NATURE OF HIGHER HOMOTOPY GROUPS 148
4.6.2 ARCWISE CONNECTEDNESS AND HIGHER HOMOTOPY GROUPS 148 4.6.3
HOMOTOPY INVARIANCE OF HIGHER HOMOTOPY GROUPS 148 4.6.4 HIGHER HOMOTOPY
GROUPS OF A PRODUCT SPACE 148 4.6.5 UNIVERSAL COVERING SPACES AND HIGHER
HOMOTOPY GROUPS 148 4.7 EXAMPLES OF HIGHER HOMOTOPY GROUPS 150 X
CONTENTS 4.8 ORDERS IN CONDENSED MATTER SYSTEMS 153 4.8.1 ORDER
PARAMETER 153 4.8.2 SUPERFLUID 4 HE AND SUPERCONDUCTORS 154 4.8.3
GENERAL CONSIDERATION 157 4.9 DEFECTS IN NEMATIC LIQUID CRYSTALS 159
4.9.1 ORDER PARAMETER OF NEMATIC LIQUID CRYSTALS 159 4.9.2 LINE DEFECTS
IN NEMATIC LIQUID CRYSTALS 160 4.9.3 POINT DEFECTS IN NEMATIC LIQUID
CRYSTALS 161 4.9.4 HIGHER DIMENSIONAL TEXTURE 162 4.10 TEXTURES IN
SUPERFLUID 3 HE-A 163 4.10.1 SUPERFLUID 3 HE-A 163 4.10.2 LINE DEFECTS
AND NON-SINGULAR VORTICES IN 3 HE-A 165 4.10.3 SHANKAR MONOPOLE IN 3
HE-A 166 PROBLEMS 167 5 MANIFOLDS 169 5.1 MANIFOLDS 169 5.1.1 HEURISTIC
INTRODUCTION 169 5.1.2 DEFINITIONS 171 5.1.3 EXAMPLES 173 5.2 THE
CALCULUS ON MANIFOLDS 178 5.2.1 DIFFERENTIABLE MAPS 179 5.2.2 VECTORS
181 5.2.3 ONE-FORMS 184 5.2.4 TENSORS 185 5.2.5 TENSOR FIELDS 185 5.2.6
INDUCED MAPS 186 5.2.7 SUBMANIFOLDS 188 5.3 FLOWS AND LIE DERIVATIVES
188 5.3.1 ONE-PARAMETER GROUP OF TRANSFORMATIONS 190 5.3.2 LIE
DERIVATIVES 191 5.4 DIFFERENTIAL FORMS 196 5.4.1 DEFINITIONS 196 5.4.2
EXTERIOR DERIVATIVES 198 5.4.3 INTERIOR PRODUCT AND LIE DERIVATIVE OF
FORMS 201 5.5 INTEGRATION OF DIFFERENTIAL FORMS 204 5.5.1 ORIENTATION *
204 5.5.2 INTEGRATION OF FORMS 205 5.6 LIE GROUPS AND LIE ALGEBRAS 207
5.6.1 LIE GROUPS 207 5.6.2 LIE ALGEBRAS 209 5.6.3 THE ONE-PARAMETER
SUBGROUP 212 5.6.4 FRAMES AND STRUCTURE EQUATION 215 5.7 THE ACTION OF
LIE GROUPS ON MANIFOLDS 216 CONTENTS XI 5.7.1 DEFINITIONS 216 5.7.2
ORBITS AND ISOTROPY GROUPS 219 5.7.3 INDUCED VECTOR FIELDS 223 5.7.4 THE
ADJOINT REPRESENTATION 224 PROBLEMS 224 6 DE RHAM COHOMOLOGY GROUPS 226
6.1 STOKES THEOREM 226 6.1.1 PRELIMINARY CONSIDERATION 226 6.1.2
STOKES THEOREM 228 6.2 DE RHAM COHOMOLOGY GROUPS 230 6.2.1 DEFINITIONS
230 6.2.2 DUALITY OF H R (M) AND H R (M); DE RHAM S THEOREM 233 6.3
POINCARE S LEMMA 235 6.4 STRUCTURE OF DE RHAM COHOMOLOGY GROUPS 237
6.4.1 POINCARE DUALITY 237 6.4.2 COHOMOLOGY RINGS 238 6.4.3 THE KUNNETH
FORMULA 238 6.4.4 PULLBACK OF DE RHAM COHOMOLOGY GROUPS 240 6.4.5
HOMOTOPY AND H L {M) 240 7 RIEMANNIAN GEOMETRY 244 7.1 RIEMANNIAN
MANIFOLDS AND PSEUDO-RIEMANNIAN MANIFOLDS 244 7.1.1 METRIC TENSORS 244
7.1.2 INDUCED METRIC 246 7.2 PARALLEL TRANSPORT, CONNECTION AND
COVARIANT DERIVATIVE 247 7.2.1 HEURISTIC INTRODUCTION 247 7.2.2 AFFINE
CONNECTIONS 249 7.2.3 PARALLEL TRANSPORT AND GEODESIES 250 7.2.4 THE
COVARIANT DERIVATIVE OF TENSOR FIELDS 251 7.2.5 THE TRANSFORMATION
PROPERTIES OF CONNECTION COEFFICIENTS 252 7.2.6 THE METRIC CONNECTION
253 7.3 CURVATURE AND TORSION 254 7.3.1 DEFINITIONS 254 7.3.2
GEOMETRICAL MEANING OF THE RIEMANN TENSOR AND THE TORSION TENSOR 256
7.3.3 THE RICCI TENSOR AND THE SCALAR CURVATURE 260 7.4 LEVI-CIVITA
CONNECTIONS 261 7.4.1 THE FUNDAMENTAL THEOREM 261 7.4.2 THE LEVI-CIVITA
CONNECTION IN THE CLASSICAL GEOMETRY OF SURFACES 262 7.4.3 GEODESIES 263
7.4.4 THE NORMAL COORDINATE SYSTEM 266 7.4.5 RIEMANN CURVATURE TENSOR
WITH LEVI-CIVITA CONNECTION 268 7.5 HOLONOMY 271 XII CONTENTS 7.6
ISOMETRIES AND CONFORMAL TRANSFORMATIONS 273 7.6.1 ISOMETRIES 273 7.6.2
CONFORMAL TRANSFORMATIONS 274 7.7 KILLING VECTOR FIELDS AND CONFORMAL
KILLING VECTOR FIELDS 279 7.7.1 KILLING VECTOR FIELDS 279 7.7.2
CONFORMAL KILLING VECTOR FIELDS 282 7.8 NON-COORDINATE BASES 283 7.8.1
DEFINITIONS 283 7.8.2 CARTAN S STRUCTURE EQUATIONS 284 7.8.3 THE LOCAL
FRAME 285 7.8.4 THE LEVI-CIVITA CONNECTION IN A NON-COORDINATE BASIS 287
7.9 DIFFERENTIAL FORMS AND HODGE THEORY 289 7.9.1 INVARIANT VOLUME
ELEMENTS 289 7.9.2 DUALITY TRANSFORMATIONS (HODGE STAR) 290 7.9.3 INNER
PRODUCTS OF R-FORMS 291 7.9.4 ADJOINTS OF EXTERIOR DERIVATIVES 293 7.9.5
THE LAPLACIAN, HARMONIC FORMS AND THE HODGE DECOMPOSITION THEOREM 294
7.9.6 HARMONIC FORMS AND DE RHAM COHOMOLOGY GROUPS 296 7.10 ASPECTS OF
GENERAL RELATIVITY 297 7.10.1 INTRODUCTION TO GENERAL RELATIVITY 297
7.10.2 EINSTEIN-HILBERT ACTION 298 7.10.3 SPINORS IN CURVED SPACETIME
300 7.11 BOSONIC STRING THEORY 302 7.11.1 THE STRING ACTION 303 7.11.2
SYMMETRIES OF THE POLYAKOV STRINGS 305 PROBLEMS 307 8 COMPLEX MANIFOLDS
308 8.1 COMPLEX MANIFOLDS 308 8.1.1 DEFINITIONS 308 8.1.2 EXAMPLES 309
8.2 CALCULUS ON COMPLEX MANIFOLDS 315 8.2.1 HOLOMORPHIC MAPS 315 8.2.2
COMPLEXIFICATIONS 316 8.2.3 ALMOST COMPLEX STRUCTURE ^ 317 8.3 COMPLEX
DIFFERENTIAL FORMS 320 8.3.1 COMPLEXIFICATION OF REAL DIFFERENTIAL FORMS
320 8.3.2 DIFFERENTIAL FORMS ON COMPLEX MANIFOLDS 321 8.3.3 DOLBEAULT
OPERATORS 322 8.4 HERMITIAN MANIFOLDS AND HERMITIAN DIFFERENTIAL
GEOMETRY 324 8.4.1 THE HERMITIAN METRIC 325 8.4.2 KAHLER FORNI 326 8.4.3
COVARIANT DERIVATIVES 327 CONTENTS XIII 8.4.4 TORSION AND CURVATURE 329
8.5 KAHLER MANIFOLDS AND KAHLER DIFFERENTIAL GEOMETRY 330 8.5.1
DEFINITIONS 330 8.5.2 KAHLER GEOMETRY 334 8.5.3 THE HOLONOMY GROUP OF
KAHLER MANIFOLDS 335 8.6 HARMONIC FORMS AND 3-COHOMOLOGY GROUPS 336
8.6.1 THE ADJOINT OPERATORS D* AND 9^ 337 8.6.2 LAPLACIANS AND THE HODGE
THEOREM 338 8.6.3 LAPLACIANS ON A KAHLER MANIFOLD 339 8.6.4 THE HODGE
NUMBERS OF KAHLER MANIFOLDS 339 8.7 ALMOST COMPLEX MANIFOLDS 341 8.7.1
DEFINITIONS 342 8.8 ORBIFOLDS 344 8.8.1 ONE-DIMENSIONAL EXAMPLES 344
8.8.2 THREE-DIMENSIONAL EXAMPLES 346 348 348 350 350 353 354 355 355 357
357 357 359 360 361 361 363 363 363 370 372 372 10 CONNECTIONS ON FIBRE
BUNDLES 374 10.1 CONNECTIONS ON PRINCIPAL BUNDLES 374 10.1.1 DEFINITIONS
375 10.1.2 THE CONNECTION ONE-FORM 376 10.1.3 THE LOCAL CONNECTION FORM
AND GAUGE POTENTIAL 377 10.1.4 HORIZONTAL LIFT AND PARALLEL TRANSPORT
381 10.2 HOLONOMY 384 FIBRE 9.1 9.2 9.3 9.4 BUNDLES TANGENT BUNDLES
FIBRE 1 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 9.2.6 BUNDLES DEFINITIONS
RECONSTRUCTION OF FIBRE BUNDLES BUNDLE MAPS EQUIVALENT BUNDLES PULLBACK
BUNDLES HOMOTOPY AXIOM VECTOR BUNDLES 9.3.1 9.3.2 9.3.3 9.3.4 9.3.5
9.3.6 DEFINITIONS AND EXAMPLES FRAMES COTANGENT BUNDLES AND DUAL BUNDLES
SECTIONS OF VECTOR BUNDLES THE PRODUCT BUNDLE AND WHITNEY SUM BUNDLE
TENSOR PRODUCT BUNDLES PRINCIPAL BUNDLES 9.4.1 9.4.2 9.4.3 DEFINITIONS
ASSOCIATED BUNDLES , TRIVIALITY OF BUNDLES PROBLEMS ** XIV CONTENTS
10.2.1 DEFINITIONS 384 10.3 CURVATURE 385 10.3.1 COVARIANT DERIVATIVES
IN PRINCIPAL BUNDLES 385 10.3.2 CURVATURE 386 10.3.3 GEOMETRICAL MEANING
OF THE CURVATURE AND THE AMBROSE- SINGER THEOREM 388 10.3.4 LOCAL FORM
OF THE CURVATURE 389 10.3.5 THE BIANCHI IDENTITY 390 10.4 THE COVARIANT
DERIVATIVE ON ASSOCIATED VECTOR BUNDLES 391 10.4.1 THE COVARIANT
DERIVATIVE ON ASSOCIATED BUNDLES 391 10.4.2 A LOCAL EXPRESSION FOR THE
COVARIANT DERIVATIVE 393 10.4.3 CURVATURE REDERIVED 396 10.4.4 A
CONNECTION WHICH PRESERVES THE INNER PRODUCT 396 10.4.5 HOLOMORPHIC
VECTOR BUNDLES AND HERMITIAN INNER PRODUCTS . 397 10.5 GAUGE THEORIES
399 10.5.1 U(L) GAUGE THEORY 399 10.5.2 THE DIRAC MAGNETIC MONOPOLE 400
10.5.3 THE AHARONOV-BOHM EFFECT * 402 10.5.4 YANG-MILLS THEORY 404
10.5.5 INSTANTONS 405 10.6 BERRY S PHASE 409 10.6.1 DERIVATION OF
BERRY S PHASE 410 10.6.2 BERRY S PHASE, BERRY S CONNECTION AND BERRY S
CURVATURE 411 PROBLEMS 418 11 CHARACTERISTIC CLASSES 419 11.1 INVARIANT
POLYNOMIALS AND THE CHERN-WEIL HOMOMORPHISM 419 11.1.1 INVARIANT
POLYNOMIALS 420 11.2 CHERN CLASSES 426 11.2.1 DEFINITIONS 426 11.2.2
PROPERTIES OF CHERN CLASSES 428 11.2.3 SPLITTING PRINCIPLE 429 11.2.4
UNIVERSAL BUNDLES AND CLASSIFYING SPACES 430 11.3 CHERN CHARACTERS 431
11.3.1 DEFINITIONS 431 11.3.2 PROPERTIES OF THE CHERN CHARACTERS 434
11.3.3 TODD CLASSES 435 11.4 PONTRJAGIN AND EULER CLASSES 436 11.4.1
PONTRJAGIN CLASSES 436 11.4.2 EULER CLASSES 439 11.4.3 HIRZEBRUCH
L-POLYNOMIAL AND A-GENUS 442 11.5 CHERN-SIMONS FORMS 443 11.5.1
DEFINITION 443 CONTENTS XV 11.5.2 THE CHERN-SIMONS FORM OF THE CHERN
CHARACTER 444 11.5.3 CARTAN S HOMOTOPY OPERATOR AND APPLICATIONS 445
11.6 STIEFEL-WHITNEY CLASSES 448 11.6.1 SPIN BUNDLES 449 11.6.2 CECH
COHOMOLOGY GROUPS 449 11.6.3 STIEFEL-WHITNEY CLASSES 450 12 INDEX
THEOREMS 453 12.1 ELLIPTIC OPERATORS AND FREDHOLM OPERATORS 453 12.1.1
ELLIPTIC OPERATORS 454 12.1.2 FREDHOLM OPERATORS 456 12.1.3 ELLIPTIC
COMPLEXES 457 12.2 THE ATIYAH-SINGER INDEX THEOREM 459 12.2.1 STATEMENT
OF THE THEOREM 459 12.3 THE DE RHAM COMPLEX 460 12.4 THE DOLBEAULT
COMPLEX 462 12.4.1 THE TWISTED DOLBEAULT COMPLEX AND THE HIRZEBRUCH-
RIEMANN-ROCH THEOREM 463 12.5 THE SIGNATURE COMPLEX 464 12.5.1 THE
HIRZEBRUCH SIGNATURE 464 12.5.2 THE SIGNATURE COMPLEX AND THE HIRZEBRUCH
SIGNATURE THEOREM 465 12.6 SPIN COMPLEXES 467 12.6.1 DIRAC OPERATOR 468
12.6.2 TWISTED SPIN COMPLEXES 471 12.7 THE HEAT KERNEL AND GENERALIZED F
-FUNCTIONS 472 12.7.1 THE HEAT KERNEL AND INDEX THEOREM 472 12.7.2
SPECTRAL F -FUNCTIONS 475 12.8 THE ATIYAH-PATODI-SINGER INDEX THEOREM
477 12.8.1 ^-INVARIANT AND SPECTRAL FLOW 477 12.8.2 THE
ATIYAH-PATODI-SINGER (APS) INDEX THEOREM 478 12.9 SUPERSYMMETRIC QUANTUM
MECHANICS 481 12.9.1 CLIFFORD ALGEBRA AND FERMIONS ** 481 12.9.2
SUPERSYMMETRIC QUANTUM MECHANICS IN FLAT SPACE 482 12.9.3 SUPERSYMMETRIC
QUANTUM MECHANICS IN A GENERAL MANIFOLD 485 12.10 SUPERSYMMETRIC PROOF
OF INDEX THEOREM 487 12.10.1 THE INDEX 487 12.10.2 PATH INTEGRAL AND
INDEX THEOREM 490 PROBLEMS 500 XVI CONTENTS 13 ANOMALIES IN GAUGE FIELD
THEORIES 501 13.1 INTRODUCTION 501 13.2 ABELIAN ANOMALIES 503 13.2.1
FUJIKAWA S METHOD 503 13.3 NON-ABELIAN ANOMALIES 508 13.4 THE
WESS-ZUMINO CONSISTENCY CONDITIONS 512 13.4.1 THE BECCHI*ROUET-STORA
OPERATOR AND THE FADDEEV- POPOV GHOST 512 13.4.2 THE BRS OPERATOR, FP
GHOST AND MODULI SPACE 513 13.4.3 THE WESS-ZUMINO CONDITIONS 515 13.4.4
DESCENT EQUATIONS AND SOLUTIONS OF WZ CONDITIONS 515 13.5 ABELIAN
ANOMALIES VERSUS NON-ABELIAN ANOMALIES 518 13.5.1 M DIMENSIONS VERSUS M
+ 2 DIMENSIONS 520 13.6 THE PARITY ANOMALY IN ODD-DIMENSIONAL SPACES 523
13.6.1 THE PARITY ANOMALY 524 13.6.2 THE DIMENSIONAL LADDER: 4-3-2 525
14 BOSONIC STRING THEORY 528 14.1 DIFFERENTIAL GEOMETRY ON RIEMANN
SURFACES 528 14.1.1 METRIC AND COMPLEX STRUCTURE * 528 14.1.2 VECTORS,
FORMS AND TENSORS 529 14.1.3 COVARIANT DERIVATIVES 531 14.1.4 THE
RIEMANN-ROCH THEOREM 533 14.2 QUANTUM THEORY OF BOSONIC STRINGS 535
14.2.1 VACUUM AMPLITUDE OF POLYAKOV STRINGS 535 14.2.2 MEASURES OF
INTEGRATION 538 14.2.3 COMPLEX TENSOR CALCULUS AND STRING MEASURE 550
14.2.4 MODULI SPACES OF RIEMANN SURFACES 554 14.3 ONE-LOOP AMPLITUDES
555 14.3.1 MODULI SPACES, CKV, BELTRAMI AND QUADRATIC DIFFERENTIALS 555
14.3.2 THE EVALUATION OF DETERMINANTS 557 REFERENCES 560 INDEX 565
|
| any_adam_object | 1 |
| author | Nakahara, Mikio |
| author_GND | (DE-588)1028332297 |
| author_facet | Nakahara, Mikio |
| author_role | aut |
| author_sort | Nakahara, Mikio |
| author_variant | m n mn |
| building | Verbundindex |
| bvnumber | BV024504878 |
| ctrlnum | (OCoLC)249349338 (DE-599)BVBBV024504878 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV024504878 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:01:00Z |
| institution | BVB |
| isbn | 0750306068 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018479442 |
| oclc_num | 249349338 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XXII, 573 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Institut of Physics Publ. |
| record_format | marc |
| series2 | Graduate student series in physics |
| spelling | Nakahara, Mikio Verfasser (DE-588)1028332297 aut Geometry, topology and physics Mikio Nakahara 2. ed. Bristol <<[u.a.]>> Institut of Physics Publ. 2003 XXII, 573 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate student series in physics Topologie (DE-588)4060425-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Topologie (DE-588)4120861-4 s Mathematische Physik (DE-588)4037952-8 s DE-604 Differentialgeometrie (DE-588)4012248-7 s Topologie (DE-588)4060425-1 s 2\p DE-604 Physik (DE-588)4045956-1 s 3\p DE-604 4\p DE-604 5\p DE-604 Differentialgleichung (DE-588)4012249-9 s 6\p DE-604 Geometrie (DE-588)4020236-7 s 7\p DE-604 Mathematische Methode (DE-588)4155620-3 s 8\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018479442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 8\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nakahara, Mikio Geometry, topology and physics Topologie (DE-588)4060425-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd Geometrie (DE-588)4020236-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4037952-8 (DE-588)4012248-7 (DE-588)4120861-4 (DE-588)4020236-7 (DE-588)4155620-3 (DE-588)4045956-1 (DE-588)4012249-9 (DE-588)4123623-3 |
| title | Geometry, topology and physics |
| title_auth | Geometry, topology and physics |
| title_exact_search | Geometry, topology and physics |
| title_full | Geometry, topology and physics Mikio Nakahara |
| title_fullStr | Geometry, topology and physics Mikio Nakahara |
| title_full_unstemmed | Geometry, topology and physics Mikio Nakahara |
| title_short | Geometry, topology and physics |
| title_sort | geometry topology and physics |
| topic | Topologie (DE-588)4060425-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Differentialgeometrie (DE-588)4012248-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd Geometrie (DE-588)4020236-7 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Topologie Mathematische Physik Differentialgeometrie Algebraische Topologie Geometrie Mathematische Methode Physik Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018479442&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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