Kontsevich's deformation quantization and quantum field theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2022]
|
| Schriftenreihe: | Lecture notes in mathematics
Volume 2311 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Preface: "... This book began as lecture notes for the course "Poisson geometry and deformation quantization" given by me during the fall semester 2020 at the University of Zurich ..." |
| Beschreibung: | xiii, 334 Seiten Illustrationen, Diagramme |
| ISBN: | 9783031051210 |
Internformat
MARC
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| 020 | |a 9783031051210 |c pb |9 978-3-031-05121-0 | ||
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| 084 | |a 81T20 |2 msc | ||
| 084 | |a 57R56 |2 msc | ||
| 084 | |a 53D17 |2 msc | ||
| 084 | |a 53D55 |2 msc | ||
| 100 | 1 | |a Moshayedi, Nima |0 (DE-588)1265721831 |4 aut | |
| 245 | 1 | 0 | |a Kontsevich's deformation quantization and quantum field theory |c Nima Moshayedi |
| 264 | 1 | |a Cham |b Springer |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a xiii, 334 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v Volume 2311 | |
| 500 | |a Preface: "... This book began as lecture notes for the course "Poisson geometry and deformation quantization" given by me during the fall semester 2020 at the University of Zurich ..." | ||
| 650 | 4 | |a Geometry, Differential. | |
| 650 | 4 | |a Manifolds (Mathematics). | |
| 650 | 4 | |a Global analysis (Mathematics). | |
| 650 | 4 | |a Quantum physics. | |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 710 | 2 | |a Poisson Geometry and Deformation Quantization, 2020, Zurich |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-05122-7 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-05123-4 |
| 830 | 0 | |a Lecture notes in mathematics |v Volume 2311 |w (DE-604)BV000676446 |9 2311 | |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033832281&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804184388494163968 |
|---|---|
| adam_text | Contents
Te ne neene nennen 1
2 Foundations of Differential Geometry 00 0000 7
2 1 Smooth Manifolds cccccccascsecussceccuseeccaucussecsases 8
211 Charts and Atlases 0 00 0 ccccccccaecuccececevecseees 8
212 Pullback and Push-forward 0 2 li
213 Tangent Space 0 ccecceececcsecuvececeuceuceeecereuss 12
2 2 Vector Fields and Differential 1-Forms ccceceecceseceous 16
221 Tangent Bundle 0 0 cccecececeueusceceseneueues 16
222 Vector Bundles cccccccescsecececeecuscucuseaseeses 17
2 2 3, Vector Fields cccceccccecuccesececatercuscesueuneas 19
224 Flow of a Vector Field 0 cc ccc eccseuccececueueees 22
225 Cotangent Bundle cccccccccescscvceseveesaueneaes 23
226 Differential 1-Forms 0ccceccuseusseecucceseases 24
2 3 Temsor Fields 0 cccccccuccucscseeceseuecaecusenscessaeeaceaes 25
231 Tensor Bundle ccccceccsacceecucaecesaseecesaneuss 25
232 Multivector Fields and Differential s-Forms 26
2 4 Integration on Manifolds and Stokes’ Theorem cc 30
241 Integration of Densities 0 cccccecascecuvaeeues 30
242 Integration of Differential Forms 33
2 4 3, Stokes’ Theorem cccccceeescecuccececcssneaeucences 36
2 5 de Rham’s Theorem ceccccccsevcaccececeseecevevecavensues 42
251 (Co)chain Complexes 0 ccccacecesucececesuceces 42
252 Singular Homology c cccecaceccaecscsecescecs 43
253 de Rham Cohomology and de Rham’s Theorem 48
2 6 Hodge Theory for Real Manifolds 0 cccccccsuceceseuecees 49
261 Riemannian Manifolds cccccceccecceceucuccuse 49
262 Hodge Dual 0 ceccceccccceccacccusensecaecaeceutceas 51
263 Hodge Decomposition 0 ccceeccaeceusceesccuseans 33
Contents
2 7 Lie Groups and Lie Algebras u ceuennenenennennneneenennnnnnnn 53
27 1 Lie Groups uuneneneeeseenessssnensnnnnnnennsennnnnnannnnnn 54
272 Lie Algebras uneeeeeneeesssssessssnssnsnnnsennnnennnnnnnnnnn 55
273 The ExponentialMap cceeneenne nenn 57
274 Smooth Actions ueueeneneenessensesnnnnsnsnnnnsenennnnnnnn 62
275 Adjoint and Coadjoint Representations 62
276 Principal Bundles 2cncsnneeen een 64
217 Lie Algebra Cohomology cuecsenneneneen nn 65
2 8 Connections and Curvature on Vector Bundles 0ecce0005 67
281 The Affine Case cnneeeessn nennen 67
282 Generalization to Vector Bundles 00a 70
283 Interpretation as Differential Forms can 72
2 9 _Distributions and Frobenius’ Theorem nnnnn 74
291 Plane Distributions euenec nn 74
292 Frobenius’ Theorem 000 75
2 10 Connections and Curvature on Principal Bundles 77
2 10 1 Vertical and Horizontal Subbundies nn 77
2 10 2 Ehresmann Connection and Curvature non 78
2 11 Basics of Category TNOOTY 0 eee ccc ceeeecceseeeescseeensneees 79
2 11 1 Definition of a Category oo eeeeccccccceesseeeneeeenees 79
211 2 Functons oo ele cee eeeceeeeceseeeeecccc ce 81
2 11 3 Monoidal Categories nn 82
Symplectic Geometry 2 222 222 2212 85
3 1 Symplectic Manifolds 0 0 00 86
311 Symplectic Form 2 00sec 86
312 Symplectic Vector Spaces nennen 87
3 13 Symplectic Manifolds 89
314 § ymplectomorphisms 00000000--00000000- eee 90
3 2 The Cotangent Bundle as a Symplectic Manifold 0c 006- 91
321 Tautological and Canonical Forms 0 ccccceeees 92
322 Symplectic Volume 00 0 93
3 3 Lagrangian Submanifolds o oo cece nn 94
331 Lagrangian Submanifolds of Cotangent Bundles - 94
33 2 Conormal Bundle u unaanaanene nn 95
333 Graphs and Symplectomorphisms au 96
34 Local Theory eeeecce cscs eese eee 97
341 Isotopies and Vector Fields oo 97
34 2 Tubular Neighborhood Theorem 99
a 100
3 5 Moser’s Theorem 0 102
351 Equivalences for Symplectic Structures 000c cccc000+ 102
352 Moser’s Trick
Contents xi
3 6 Weinstein’s Tubular Neighborhood Theorem c0ece0cc05 106
361 Weinstein’s Lagrangian Neighborhood Theorem 106
362 Weinstein’s Tubular Neighborhood Theorem 107
363 Some Applications cccccceuccavececeeseucceceuees 108
3 7 Classical Mechanics cccccccecseccusceuccussccuuvensense 111
371 Lagrangian Mechanics and Variational Principle 111
372 Hamiltonian and Symplectic Vector Fields 114
373 Hamiltonian Mechanics nen 115
374 Relation of Lie Brackets and Further Structure 116
375 Integrable Systems cccccceececececceceeceuceucces 118
3 8 Moment Maps ccceeccsccuscucsecscacsceseuceceuseaseuss 122
381 Symplectic and Hamiltonian Actions nn: 122
382 Hamiltonian Actions IT and Moment Maps 123
3 9 Symplectic Reduction ccccccscecceceuccessuscaecescenees 124
391 Quotient Manifold by Group Action 124
392 The Marsden-Weinstein Theorem nenn 127
393 Noether’s Theorem ceneeceneananneenneene nennen 130
3 10 Kahler Manifolds and Complex Geometry cccecceeeueees 130
3 10 1 Complex Structures 0 0 00 cccccececeseuscecncnesesaceeees 130
3 10 2 Kahler Manifolds cccccccccaceseencceueeeeeaees 131
3 11 Hodge Theory for Complex Manifolds ceccecucceceeees 136
3 11 1 Hodge Dual and Hodge Laplacian cn 136
3 11 2 Hodge Decomposition and Hodge Diamond 137
4 Poisson Geometry cccccceccecasccsccucuecevccecueseuseecaecense 141
4 1 Poisson Manifolds cccececescecescvccscuenscecusaeeesenenens 142
411 Poisson Structures and the Schouten-Nijenhuis
Bracket cc cscececececsensnseeeeceeeaseeceseecensuneensnens 142
412| Examples of Poisson Structures 0cccseseceeees 143
4 2 Symplectic Leaves and Local Structure of Poisson Manifolds 145
421 Local and Regular Poisson Structures 0 0 0005 145
422 Local Splitting and Symplectic Foliation 146
4 3 Poisson Morphisms and Completeness cccceceseeveaeeeee 148
4 4 Poisson Cohomology - cscssecuseeececeuceuctecaucessascass 150
441 Definition and Existence c cccseeceaeceeueeeuss 150
442 Interpretation unensenensesunnensenenennennennennenne nenn 151
45 _Symplectic Groupoids and Integration of Poisson Manifolds 153
451 Lie Algebroids and Lie Groupoids 0 0c0008 153
452 Symplectic Groupoids and Integrability Conditions 155
4 6 Dirac Manifolds 2222unseenenneennennnnnenenenenneneneneenneen 157
461 Courant Algebroids ccccccccccesecvacececsecesuens 157
462 Dirac Structures 0 ccececcccsseuecnecevcaeeuscuseance 158
463 Dirac Structures for Constrained Manifolds +- 159
4 7 Morita Equivalence for Poisson Manifolds 00cceccveceeeus 160
471 Morita Equivalence of Symplectic Groupoids 161
Contents
472_ Morita Equivalence of Poisson Manifolds 161
4 7 3, Symplectic Realization of Morita Equivalent
Poisson Manifolds cnnenenee nn 163
5 Deformation Quantization 00c ce ec cee teeeteceeeces , 165
S L Star Products uuccnnenssescsennessnnnnsnnsessnensnennennnnnnnnnn 166
511 Formal Power Series uananance nennen 166
512 Formal Deformations en 168
5 13 The Moyal Product 2ceeenesnneeneee nn 170
514 The Canonical Star Product on g* una 171
515 Equivalent Star Products eu 172
516 Fedosov’s Globalization Approach 0 nn 174
517 Symmetries of Star Products cn 181
518 »-Hamiltonians and Quantum Moment Maps 5 182
5 2 Formality 2000 ccc cccecccecceescceceueccavececeseavestustettessees 184
521 Some Formal Setup 0 0 cccccceeeeceeecueceeceeseres 184
522 Differential Graded Lie Algebras 0 000ccc cseees 185
5 2 30 Loo-Algebras c c cc cececececaccesesceceucueeeueeters 187
5 24 The DGLA of Multivector Fields V n- 192
525 The DGLA of Multidifferential Operators D - 193
526 The Hochschild-Kostant-Rosenberg Map 198
527 The Dual Point of View cenoeeeeeennenen ern 199
528 Formality of D and Classification of Star Products
ORG nennnnennnsnnene sense nennen nee 2
53_ Kontsevich’s Star Product een 8
534 Data for the Construction ee er I
532 Proof of Kontsevich’s Formula 518
533 Logarithmic Formality eeneeetetetet 9
5 4 Globalization of Kontsevich’s Star Product et 519
541 The Product, Connection and Curvature Maps et 2
542 Construction of Solutions for a Fedosov-Type Equation 224
5 5 Operadic Approach to Formality and Deligne’s Conjecture --++: 524
551 Operads and Algebras een 226
552 Topological Operads een 327
553 TheLittle Disks Operad ent] 328
554 Deligne’s Conjecture een
555 Formality of Chain Operads and Relation to 29
Deformation Quantization een 1
6 Quantum Field Theoretic Approach to Deformation Quantization ---
6 1 The Atiyah-Segal Definition of a Functorial Quantum 234
Field Theory 2eeeeeennnenenenne nennt en 936
6 2 Feynman Path Integrals and Perturbative Quantum Field Theor 236
621 Functional Integrals and Expectation Values 7 237
622 Gaussian Integrals een 240
623 Integration of Grassmann Variables
Contents
6 3 The Moyal Product as a Path Integral Quantization -
631 The Propagator e ceeenseneneensennnenenenanennen en aennn
632 Expectation Values ceeeeeennnenener ernennen
633 Digression on the Divergence of Vector Fields
634 Independence of Evaluation Points s +-eseeeeees
635 ASSOCIALIVILY 00 cee cece cece cere eee ee ere ere e nner n ates
636 The Evolution Operator as an Application err r -
637 _Perturbative Evaluation of Integrals „oerrereenee
638 Feynman Diagrams and Perturbative Expansion
639 Infinite-Dimensional Case , 60cceceseee rete ene eeees
6 3 10 Generalizing the Expansion 6: csssseeeeeee eee et ees
6 4 Symmetries and Gauge Formalisms een
641 The Main Construction: Faddeev-Popov
Ghost Method ::secese eee ee eet e renee ne reer ene nee ens
642 The BRST Formalism c:seeee eee eee ener renee
64 3 _ Infinite-Dimensional Case -- neenereeeneenenn nn
6 5 The Poisson Sigma Model eenenenenenennnennnnanennne
651 Formulation ofthe Model --neneneenenenennen
652 Observables seees essen sten rennen seen onen ent
6 6 Phase Space Geometry and Symplectic Groupoids :0:00+
661 Hamiltonian Formulation of the Poisson Sigma Model
662 The Phase Space and Its Symplectic Groupoid
SUPUCtUTe 0 cece cece cece eee teen tence ee eaeeeeneeeenaes
6 7 Deformation Quantization for Affine Poisson Structures +
671 Gauge-Fixing and Feynman Diagrams een
672 Independence of the Evaluation Point eneee
673 ASSOCIALIVILY 6 cece cece eee eee nent rennet enna nent etn e ees
6 8 The Cattaneo—Felder Construction - ceeeeeceee rere rere ene ee es
681 Supermanifolds and Graded Manifolds 00
682 The Batalin-Vilkovisky Formalism eeeensenenns
6 83 _Formulation of the Main Theorem „user sersenee
6 84 Proof Sketch of the Main Theorem een
685 Other Similar Constructions eenerseeeneneneen nennen
69A More General Approach: The AKSZ Construction
691 Differential Graded Symplectic Hamiltonian Manifolds
692 AKSZ Sigma Models --s:cseceeeeeeeeener esses nenes
D331) (2) 9 |) ea
Index cccccceecceeneneeeneeeeeennee nen nenn nennen nannten nennen tn
|
| adam_txt |
Contents
Te ne neene nennen 1
2 Foundations of Differential Geometry 00 0000 7
2 1 Smooth Manifolds cccccccascsecussceccuseeccaucussecsases 8
211 Charts and Atlases 0 00 0 ccccccccaecuccececevecseees 8
212 Pullback and Push-forward 0 2 li
213 Tangent Space 0 ccecceececcsecuvececeuceuceeecereuss 12
2 2 Vector Fields and Differential 1-Forms ccceceecceseceous 16
221 Tangent Bundle 0 0 cccecececeueusceceseneueues 16
222 Vector Bundles cccccccescsecececeecuscucuseaseeses 17
2 2 3, Vector Fields cccceccccecuccesececatercuscesueuneas 19
224 Flow of a Vector Field 0 cc ccc eccseuccececueueees 22
225 Cotangent Bundle cccccccccescscvceseveesaueneaes 23
226 Differential 1-Forms 0ccceccuseusseecucceseases 24
2 3 Temsor Fields 0 cccccccuccucscseeceseuecaecusenscessaeeaceaes 25
231 Tensor Bundle ccccceccsacceecucaecesaseecesaneuss 25
232 Multivector Fields and Differential s-Forms 26
2 4 Integration on Manifolds and Stokes’ Theorem cc 30
241 Integration of Densities 0 cccccecascecuvaeeues 30
242 Integration of Differential Forms 33
2 4 3, Stokes’ Theorem cccccceeescecuccececcssneaeucences 36
2 5 de Rham’s Theorem ceccccccsevcaccececeseecevevecavensues 42
251 (Co)chain Complexes 0 ccccacecesucececesuceces 42
252 Singular Homology c cccecaceccaecscsecescecs 43
253 de Rham Cohomology and de Rham’s Theorem 48
2 6 Hodge Theory for Real Manifolds 0 cccccccsuceceseuecees 49
261 Riemannian Manifolds cccccceccecceceucuccuse 49
262 Hodge Dual 0 ceccceccccceccacccusensecaecaeceutceas 51
263 Hodge Decomposition 0 ccceeccaeceusceesccuseans 33
Contents
2 7 Lie Groups and Lie Algebras u ceuennenenennennneneenennnnnnnn 53
27 1 Lie Groups uuneneneeeseenessssnensnnnnnnennsennnnnnannnnnn 54
272 Lie Algebras uneeeeeneeesssssessssnssnsnnnsennnnennnnnnnnnnn 55
273 The ExponentialMap cceeneenne nenn 57
274 Smooth Actions ueueeneneenessensesnnnnsnsnnnnsenennnnnnnn 62
275 Adjoint and Coadjoint Representations 62
276 Principal Bundles 2cncsnneeen een 64
217 Lie Algebra Cohomology cuecsenneneneen nn 65
2 8 Connections and Curvature on Vector Bundles 0ecce0005 67
281 The Affine Case cnneeeessn nennen 67
282 Generalization to Vector Bundles 00a 70
283 Interpretation as Differential Forms can 72
2 9 _Distributions and Frobenius’ Theorem nnnnn 74
291 Plane Distributions euenec nn 74
292 Frobenius’ Theorem 000 75
2 10 Connections and Curvature on Principal Bundles 77
2 10 1 Vertical and Horizontal Subbundies nn 77
2 10 2 Ehresmann Connection and Curvature non 78
2 11 Basics of Category TNOOTY 0 eee ccc ceeeecceseeeescseeensneees 79
2 11 1 Definition of a Category oo eeeeccccccceesseeeneeeenees 79
211 2 Functons oo ele cee eeeceeeeceseeeeecccc ce 81
2 11 3 Monoidal Categories nn 82
Symplectic Geometry 2 222 222 2212 85
3 1 Symplectic Manifolds 0 0 00 86
311 Symplectic Form 2 00sec 86
312 Symplectic Vector Spaces nennen 87
3 13 Symplectic Manifolds 89
314 § ymplectomorphisms 00000000--00000000- eee 90
3 2 The Cotangent Bundle as a Symplectic Manifold 0c 006- 91
321 Tautological and Canonical Forms 0 ccccceeees 92
322 Symplectic Volume 00 0 93
3 3 Lagrangian Submanifolds o oo cece nn 94
331 Lagrangian Submanifolds of Cotangent Bundles - 94
33 2 Conormal Bundle u unaanaanene nn 95
333 Graphs and Symplectomorphisms au 96
34 Local Theory eeeecce cscs eese eee 97
341 Isotopies and Vector Fields oo 97
34 2 Tubular Neighborhood Theorem 99
a 100
3 5 Moser’s Theorem 0 102
351 Equivalences for Symplectic Structures 000c cccc000+ 102
352 Moser’s Trick
Contents xi
3 6 Weinstein’s Tubular Neighborhood Theorem c0ece0cc05 106
361 Weinstein’s Lagrangian Neighborhood Theorem 106
362 Weinstein’s Tubular Neighborhood Theorem 107
363 Some Applications cccccceuccavececeeseucceceuees 108
3 7 Classical Mechanics cccccccecseccusceuccussccuuvensense 111
371 Lagrangian Mechanics and Variational Principle 111
372 Hamiltonian and Symplectic Vector Fields 114
373 Hamiltonian Mechanics nen 115
374 Relation of Lie Brackets and Further Structure 116
375 Integrable Systems cccccceececececceceeceuceucces 118
3 8 Moment Maps ccceeccsccuscucsecscacsceseuceceuseaseuss 122
381 Symplectic and Hamiltonian Actions nn: 122
382 Hamiltonian Actions IT and Moment Maps 123
3 9 Symplectic Reduction ccccccscecceceuccessuscaecescenees 124
391 Quotient Manifold by Group Action 124
392 The Marsden-Weinstein Theorem nenn 127
393 Noether’s Theorem ceneeceneananneenneene nennen 130
3 10 Kahler Manifolds and Complex Geometry cccecceeeueees 130
3 10 1 Complex Structures 0 0 00 cccccececeseuscecncnesesaceeees 130
3 10 2 Kahler Manifolds cccccccccaceseencceueeeeeaees 131
3 11 Hodge Theory for Complex Manifolds ceccecucceceeees 136
3 11 1 Hodge Dual and Hodge Laplacian cn 136
3 11 2 Hodge Decomposition and Hodge Diamond 137
4 Poisson Geometry cccccceccecasccsccucuecevccecueseuseecaecense 141
4 1 Poisson Manifolds cccececescecescvccscuenscecusaeeesenenens 142
411 Poisson Structures and the Schouten-Nijenhuis
Bracket cc cscececececsensnseeeeceeeaseeceseecensuneensnens 142
412| Examples of Poisson Structures 0cccseseceeees 143
4 2 Symplectic Leaves and Local Structure of Poisson Manifolds 145
421 Local and Regular Poisson Structures 0 0 0005 145
422 Local Splitting and Symplectic Foliation 146
4 3 Poisson Morphisms and Completeness cccceceseeveaeeeee 148
4 4 Poisson Cohomology - cscssecuseeececeuceuctecaucessascass 150
441 Definition and Existence c cccseeceaeceeueeeuss 150
442 Interpretation unensenensesunnensenenennennennennenne nenn 151
45 _Symplectic Groupoids and Integration of Poisson Manifolds 153
451 Lie Algebroids and Lie Groupoids 0 0c0008 153
452 Symplectic Groupoids and Integrability Conditions 155
4 6 Dirac Manifolds 2222unseenenneennennnnnenenenenneneneneenneen 157
461 Courant Algebroids ccccccccccesecvacececsecesuens 157
462 Dirac Structures 0 ccececcccsseuecnecevcaeeuscuseance 158
463 Dirac Structures for Constrained Manifolds +- 159
4 7 Morita Equivalence for Poisson Manifolds 00cceccveceeeus 160
471 Morita Equivalence of Symplectic Groupoids 161
Contents
472_ Morita Equivalence of Poisson Manifolds 161
4 7 3, Symplectic Realization of Morita Equivalent
Poisson Manifolds cnnenenee nn 163
5 Deformation Quantization 00c ce ec cee teeeteceeeces , 165
S L Star Products uuccnnenssescsennessnnnnsnnsessnensnennennnnnnnnnn 166
511 Formal Power Series uananance nennen 166
512 Formal Deformations en 168
5 13 The Moyal Product 2ceeenesnneeneee nn 170
514 The Canonical Star Product on g* una 171
515 Equivalent Star Products eu 172
516 Fedosov’s Globalization Approach 0 nn 174
517 Symmetries of Star Products cn 181
518 »-Hamiltonians and Quantum Moment Maps 5 182
5 2 Formality 2000 ccc cccecccecceescceceueccavececeseavestustettessees 184
521 Some Formal Setup 0 0 cccccceeeeceeecueceeceeseres 184
522 Differential Graded Lie Algebras 0 000ccc cseees 185
5 2 30 Loo-Algebras c c cc cececececaccesesceceucueeeueeters 187
5 24 The DGLA of Multivector Fields V n- 192
525 The DGLA of Multidifferential Operators D - 193
526 The Hochschild-Kostant-Rosenberg Map 198
527 The Dual Point of View cenoeeeeeennenen ern 199
528 Formality of D and Classification of Star Products
ORG nennnnennnsnnene sense nennen nee 2
53_ Kontsevich’s Star Product een 8
534 Data for the Construction ee er I
532 Proof of Kontsevich’s Formula 518
533 Logarithmic Formality eeneeetetetet 9
5 4 Globalization of Kontsevich’s Star Product et 519
541 The Product, Connection and Curvature Maps et 2
542 Construction of Solutions for a Fedosov-Type Equation 224
5 5 Operadic Approach to Formality and Deligne’s Conjecture --++: 524
551 Operads and Algebras een 226
552 Topological Operads een 327
553 TheLittle Disks Operad ent] 328
554 Deligne’s Conjecture een
555 Formality of Chain Operads and Relation to 29
Deformation Quantization een 1
6 Quantum Field Theoretic Approach to Deformation Quantization ---
6 1 The Atiyah-Segal Definition of a Functorial Quantum 234
Field Theory 2eeeeeennnenenenne nennt en 936
6 2 Feynman Path Integrals and Perturbative Quantum Field Theor 236
621 Functional Integrals and Expectation Values 7 237
622 Gaussian Integrals een 240
623 Integration of Grassmann Variables
Contents
6 3 The Moyal Product as a Path Integral Quantization -
631 The Propagator e ceeenseneneensennnenenenanennen en aennn
632 Expectation Values ceeeeeennnenener ernennen
633 Digression on the Divergence of Vector Fields
634 Independence of Evaluation Points s +-eseeeeees
635 ASSOCIALIVILY 00 cee cece cece cere eee ee ere ere e nner n ates
636 The Evolution Operator as an Application err r -
637 _Perturbative Evaluation of Integrals „oerrereenee
638 Feynman Diagrams and Perturbative Expansion
639 Infinite-Dimensional Case , 60cceceseee rete ene eeees
6 3 10 Generalizing the Expansion 6: csssseeeeeee eee et ees
6 4 Symmetries and Gauge Formalisms een
641 The Main Construction: Faddeev-Popov
Ghost Method ::secese eee ee eet e renee ne reer ene nee ens
642 The BRST Formalism c:seeee eee eee ener renee
64 3 _ Infinite-Dimensional Case -- neenereeeneenenn nn
6 5 The Poisson Sigma Model eenenenenenennnennnnanennne
651 Formulation ofthe Model --neneneenenenennen
652 Observables seees essen sten rennen seen onen ent
6 6 Phase Space Geometry and Symplectic Groupoids :0:00+
661 Hamiltonian Formulation of the Poisson Sigma Model
662 The Phase Space and Its Symplectic Groupoid
SUPUCtUTe 0 cece cece cece eee teen tence ee eaeeeeneeeenaes
6 7 Deformation Quantization for Affine Poisson Structures +
671 Gauge-Fixing and Feynman Diagrams een
672 Independence of the Evaluation Point eneee
673 ASSOCIALIVILY 6 cece cece eee eee nent rennet enna nent etn e ees
6 8 The Cattaneo—Felder Construction - ceeeeeceee rere rere ene ee es
681 Supermanifolds and Graded Manifolds 00
682 The Batalin-Vilkovisky Formalism eeeensenenns
6 83 _Formulation of the Main Theorem „user sersenee
6 84 Proof Sketch of the Main Theorem een
685 Other Similar Constructions eenerseeeneneneen nennen
69A More General Approach: The AKSZ Construction
691 Differential Graded Symplectic Hamiltonian Manifolds
692 AKSZ Sigma Models --s:cseceeeeeeeeener esses nenes
D331) (2) 9 |) ea
Index cccccceecceeneneeeneeeeeennee nen nenn nennen nannten nennen tn |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Moshayedi, Nima |
| author_GND | (DE-588)1265721831 |
| author_facet | Moshayedi, Nima |
| author_role | aut |
| author_sort | Moshayedi, Nima |
| author_variant | n m nm |
| building | Verbundindex |
| bvnumber | BV048454180 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)1344245339 (DE-599)HBZHT021461583 |
| dewey-raw | a516.36c23 |
| dewey-search | a516.36c23 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift |
| id | DE-604.BV048454180 |
| illustrated | Illustrated |
| index_date | 2024-07-03T20:31:51Z |
| indexdate | 2024-07-10T09:38:33Z |
| institution | BVB |
| isbn | 9783031051210 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033832281 |
| oclc_num | 1344245339 |
| open_access_boolean | |
| owner | DE-188 DE-824 DE-83 DE-20 |
| owner_facet | DE-188 DE-824 DE-83 DE-20 |
| physical | xiii, 334 Seiten Illustrationen, Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Moshayedi, Nima (DE-588)1265721831 aut Kontsevich's deformation quantization and quantum field theory Nima Moshayedi Cham Springer [2022] © 2022 xiii, 334 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2311 Preface: "... This book began as lecture notes for the course "Poisson geometry and deformation quantization" given by me during the fall semester 2020 at the University of Zurich ..." Geometry, Differential. Manifolds (Mathematics). Global analysis (Mathematics). Quantum physics. (DE-588)1071861417 Konferenzschrift gnd-content Poisson Geometry and Deformation Quantization, 2020, Zurich Sonstige oth Erscheint auch als Online-Ausgabe 978-3-031-05122-7 Erscheint auch als Online-Ausgabe 978-3-031-05123-4 Lecture notes in mathematics Volume 2311 (DE-604)BV000676446 2311 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033832281&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moshayedi, Nima Kontsevich's deformation quantization and quantum field theory Lecture notes in mathematics Geometry, Differential. Manifolds (Mathematics). Global analysis (Mathematics). Quantum physics. |
| subject_GND | (DE-588)1071861417 |
| title | Kontsevich's deformation quantization and quantum field theory |
| title_auth | Kontsevich's deformation quantization and quantum field theory |
| title_exact_search | Kontsevich's deformation quantization and quantum field theory |
| title_exact_search_txtP | Kontsevich's deformation quantization and quantum field theory |
| title_full | Kontsevich's deformation quantization and quantum field theory Nima Moshayedi |
| title_fullStr | Kontsevich's deformation quantization and quantum field theory Nima Moshayedi |
| title_full_unstemmed | Kontsevich's deformation quantization and quantum field theory Nima Moshayedi |
| title_short | Kontsevich's deformation quantization and quantum field theory |
| title_sort | kontsevich s deformation quantization and quantum field theory |
| topic | Geometry, Differential. Manifolds (Mathematics). Global analysis (Mathematics). Quantum physics. |
| topic_facet | Geometry, Differential. Manifolds (Mathematics). Global analysis (Mathematics). Quantum physics. Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033832281&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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