Factorization algebras in quantum field theory: Volume 2 Factorization algebras in quantum field theory
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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Cambridge
Cambridge University Press
2021
|
| Series: | New mathematical monographs
41 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 402 Seiten |
| ISBN: | 9781107163157 |
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| 245 | 1 | 0 | |a Factorization algebras in quantum field theory |n Volume 2 |p Factorization algebras in quantum field theory |c Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
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Record in the Search Index
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Contents Contents of Volume 1 1 page xi Introduction and Overview 1.1 The Factorization Algebra of Classical Observables 1.2 The Factorization Algebra of Quantum Observables 1.3 The Physical Importance of Factorization Algebras 1.4 Poisson Structures and Deformation Quantization 1.5 The Noether Theorem 1.6 Brief Orienting Remarks toward the Literature 1.7 Acknowledgments PARTI CLASSICAL FIELD THEORY 1 1 2 3 6 8 11 12 15 2 Introduction to Classical Field Theory 2.1 The Euler-Lagrange Equations 2.2 Observables 2.3 The Symplectic Structure 2.4 The Pq Structure 17 17 18 19 19 3 Elliptic Moduli Problems 3.1 Formal Moduli Problems and Lie Algebras 3.2 Examples of Elliptic Moduli ProblemsRelated to Scalar Field Theories 3.3 Examples of Elliptic Moduli ProblemsRelated to Gauge Theories 3.4 Cochains of a Local Algebra 3.5 D-modules and Local Algebras 20 21 vii 25 28 32 34
Contents viii 4 The Classical Batalin-Vilkovisky Formalism 4.1 The Classical BV Formalism in Finite Dimensions 4.2 The Classical BV Formalism in Infinite Dimensions 4.3 The Derived Critical Locus of an Action Functional 4.4 A Succinct Definition of a Classical Field Theory 4.5 Examples of Scalar Field Theories from Action Functionals 4.6 Cotangent Field Theories 5 The Observables of a Classical Field Theory 5.1 5.2 5.3 5.4 The Factorization Algebra of Classical Observables The Graded Poisson Structure on Classical Observables The Poisson Structure for Free Field Theories The Poisson Structure for a General Classical Field Theory PARTII 6 QUANTUM FIELD THEORY Introduction to Quantum Field Theory 6.1 The Quantum ВV Formalism in Finite Dimensions 6.2 The “Free Scalar Field” in Finite Dimensions 6.3 An Operadic Description 6.4 Equivariant BD Quantization and Volume Forms 6.5 How Renormalization Group Flow Interlocks with the BV Formalism 83 6.6 Overview of the Rest of This Part 7 Effective Field Theories and Batalin-Vilkovisky Quantization 7.1 7.2 7.3 7.4 7.5 8 Local Action Functionals The Definition of a Quantum Field Theory Families of Theories over Nilpotent dg Manifolds The Simplicial Set of Theories The Theorem on Quantization The Observables of a Quantum Field Theory 8.1 Free Fields 8.2 8.3 8.4 8.5 8.6 8.7 The BD Algebra of Global Observables Global Observables Local Observables Local Observables Form a Prefactorization Algebra Local Observables Form a Factorization Algebra The Map from Theories to Factorization Algebras Is a Map of Presheaves 138 43 43 45 48 54 57 58 63
63 64 66 68 73 75 76 79 81 82 84 86 87 88 99 105 Ю9 111 111 115 124 126 128 132
Contents 9 ix Further Aspects of Quantum Observables 144 9.1 Translation Invariance for Field Theories and Observables 144 9.2 Holomorphically Translation-Invariant Theories and Observables 148 9.3 Renormalizability and Factorization Algebras 154 9.4 Cotangent Theories and Volume Forms 168 9.5 Correlation Functions 177 10 Operator Product Expansions, with Examples 10.1 Point Observables 10.2 The Operator Product Expansion 10.3 The OPE to First Order in ћ 10.4 The OPE in the 04 Theory 10.5 The Operator Product for Holomorphic Theories 10.6 Quantum Groups and Higher-DimensionalGauge Theories PART III A FACTORIZATION ENHANCEMENT OF THE NOETHER THEOREM 179 179 185 188 197 201 210 225 11 Introduction to the Noether Theorems 227 11.1 Symmetries in the Classical B V Formalism 228 11.2 Koszul Duality and Symmetries via the Classical Master Equation 233 11.3 Symmetries in the Quantum BV Formalism 239 12 The Noether Theorem in Classical Field Theory 12.1 An Overview of the Main Theorem 12.2 Symmetries of a Classical Field Theory 12.3 The Factorization Algebra of Equivariant Classical Observables 259 12.4 The Classical Noether Theorem 12.5 Conserved Currents 12.6 Examples of the Classical Noether Theorem 12.7 The Noether Theorem and the Operator Product Expansion 245 245 246 263 268 270 279 13 The Noether Theorem in Quantum Field Theory 289 13.1 The Quantum Noether Theorem 289 13.2 Actions of a Local Algebra on a Quantum Field Theory 294 13.3 Obstruction Theory for Quantizing Equivariant Theories 299 13.4 The Factorization Algebra of an Equivariant Quantum Field Theory 303 13.5 The
Quantum Noether Theorem Redux 304
Contents x 13.6 Trivializing the Action on Factorization Homology 13.7 The Noether Theorem and the Local Index Theorem 13.8 The Partition Function and the Quantum Noether Theorem 14 Examples of the Noether Theorems 14.1 Examples from Mechanics 14.2 Examples from Chiral Conformal Field Theory 14.3 An Example from Topological Field Theory 313 314 323 325 325 344 354 Appendix A Background 360 Appendix В Functions on Spaces of Sections 375 Appendix C A Formal Darboux Lemma 385 References Index 393 399 |
| adam_txt |
Contents Contents of Volume 1 1 page xi Introduction and Overview 1.1 The Factorization Algebra of Classical Observables 1.2 The Factorization Algebra of Quantum Observables 1.3 The Physical Importance of Factorization Algebras 1.4 Poisson Structures and Deformation Quantization 1.5 The Noether Theorem 1.6 Brief Orienting Remarks toward the Literature 1.7 Acknowledgments PARTI CLASSICAL FIELD THEORY 1 1 2 3 6 8 11 12 15 2 Introduction to Classical Field Theory 2.1 The Euler-Lagrange Equations 2.2 Observables 2.3 The Symplectic Structure 2.4 The Pq Structure 17 17 18 19 19 3 Elliptic Moduli Problems 3.1 Formal Moduli Problems and Lie Algebras 3.2 Examples of Elliptic Moduli ProblemsRelated to Scalar Field Theories 3.3 Examples of Elliptic Moduli ProblemsRelated to Gauge Theories 3.4 Cochains of a Local Algebra 3.5 D-modules and Local Algebras 20 21 vii 25 28 32 34
Contents viii 4 The Classical Batalin-Vilkovisky Formalism 4.1 The Classical BV Formalism in Finite Dimensions 4.2 The Classical BV Formalism in Infinite Dimensions 4.3 The Derived Critical Locus of an Action Functional 4.4 A Succinct Definition of a Classical Field Theory 4.5 Examples of Scalar Field Theories from Action Functionals 4.6 Cotangent Field Theories 5 The Observables of a Classical Field Theory 5.1 5.2 5.3 5.4 The Factorization Algebra of Classical Observables The Graded Poisson Structure on Classical Observables The Poisson Structure for Free Field Theories The Poisson Structure for a General Classical Field Theory PARTII 6 QUANTUM FIELD THEORY Introduction to Quantum Field Theory 6.1 The Quantum ВV Formalism in Finite Dimensions 6.2 The “Free Scalar Field” in Finite Dimensions 6.3 An Operadic Description 6.4 Equivariant BD Quantization and Volume Forms 6.5 How Renormalization Group Flow Interlocks with the BV Formalism 83 6.6 Overview of the Rest of This Part 7 Effective Field Theories and Batalin-Vilkovisky Quantization 7.1 7.2 7.3 7.4 7.5 8 Local Action Functionals The Definition of a Quantum Field Theory Families of Theories over Nilpotent dg Manifolds The Simplicial Set of Theories The Theorem on Quantization The Observables of a Quantum Field Theory 8.1 Free Fields 8.2 8.3 8.4 8.5 8.6 8.7 The BD Algebra of Global Observables Global Observables Local Observables Local Observables Form a Prefactorization Algebra Local Observables Form a Factorization Algebra The Map from Theories to Factorization Algebras Is a Map of Presheaves 138 43 43 45 48 54 57 58 63
63 64 66 68 73 75 76 79 81 82 84 86 87 88 99 105 Ю9 111 111 115 124 126 128 132
Contents 9 ix Further Aspects of Quantum Observables 144 9.1 Translation Invariance for Field Theories and Observables 144 9.2 Holomorphically Translation-Invariant Theories and Observables 148 9.3 Renormalizability and Factorization Algebras 154 9.4 Cotangent Theories and Volume Forms 168 9.5 Correlation Functions 177 10 Operator Product Expansions, with Examples 10.1 Point Observables 10.2 The Operator Product Expansion 10.3 The OPE to First Order in ћ 10.4 The OPE in the 04 Theory 10.5 The Operator Product for Holomorphic Theories 10.6 Quantum Groups and Higher-DimensionalGauge Theories PART III A FACTORIZATION ENHANCEMENT OF THE NOETHER THEOREM 179 179 185 188 197 201 210 225 11 Introduction to the Noether Theorems 227 11.1 Symmetries in the Classical B V Formalism 228 11.2 Koszul Duality and Symmetries via the Classical Master Equation 233 11.3 Symmetries in the Quantum BV Formalism 239 12 The Noether Theorem in Classical Field Theory 12.1 An Overview of the Main Theorem 12.2 Symmetries of a Classical Field Theory 12.3 The Factorization Algebra of Equivariant Classical Observables 259 12.4 The Classical Noether Theorem 12.5 Conserved Currents 12.6 Examples of the Classical Noether Theorem 12.7 The Noether Theorem and the Operator Product Expansion 245 245 246 263 268 270 279 13 The Noether Theorem in Quantum Field Theory 289 13.1 The Quantum Noether Theorem 289 13.2 Actions of a Local Algebra on a Quantum Field Theory 294 13.3 Obstruction Theory for Quantizing Equivariant Theories 299 13.4 The Factorization Algebra of an Equivariant Quantum Field Theory 303 13.5 The
Quantum Noether Theorem Redux 304
Contents x 13.6 Trivializing the Action on Factorization Homology 13.7 The Noether Theorem and the Local Index Theorem 13.8 The Partition Function and the Quantum Noether Theorem 14 Examples of the Noether Theorems 14.1 Examples from Mechanics 14.2 Examples from Chiral Conformal Field Theory 14.3 An Example from Topological Field Theory 313 314 323 325 325 344 354 Appendix A Background 360 Appendix В Functions on Spaces of Sections 375 Appendix C A Formal Darboux Lemma 385 References Index 393 399 |
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| spelling | Costello, Kevin 1977- Verfasser (DE-588)1020383682 aut Factorization algebras in quantum field theory Volume 2 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst Cambridge Cambridge University Press 2021 xiii, 402 Seiten txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 41 Gwilliam, Owen Verfasser (DE-588)1127755161 aut (DE-604)BV044036120 2 New mathematical monographs 41 (DE-604)BV035420183 41 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032907210&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Costello, Kevin 1977- Costello, Kevin 1977- Gwilliam, Owen Gwilliam, Owen Factorization algebras in quantum field theory New mathematical monographs |
| title | Factorization algebras in quantum field theory |
| title_auth | Factorization algebras in quantum field theory |
| title_exact_search | Factorization algebras in quantum field theory |
| title_exact_search_txtP | Factorization algebras in quantum field theory |
| title_full | Factorization algebras in quantum field theory Volume 2 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
| title_fullStr | Factorization algebras in quantum field theory Volume 2 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
| title_full_unstemmed | Factorization algebras in quantum field theory Volume 2 Factorization algebras in quantum field theory Kevin Costello, Perimeter Institute for Theoretical Physics, Waterloo, Ontario; Owen Gwilliam, Max-Planck-Institut for Mathematics, Bonn, University of Massachusetts, Amherst |
| title_short | Factorization algebras in quantum field theory |
| title_sort | factorization algebras in quantum field theory factorization algebras in quantum field theory |
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