Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource (XVII, 421 Seiten) , Illustrationen, Diagramme

ISBN: 9783030653217

Series Statement: Lecture Notes in Physics 980

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-65320-0

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-65322-4

Language: English

Subjects: Physics

DOI: 10.1007/978-3-030-65321-7

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

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Format: [3] Bl., 22 S. , 4°

Note: Fingerprint nach Ex. der HAAB Weimar , Vorlageform des Erscheinungsvermerks: Francofurti ad Viadrum Typis Joannis Christiani Winteri Acad. Reg. Typogr. - Erscheinungsjahr nach Datierung der Dissertation , Frankfurt (Oder), Phil. Diss., 1765

Additional Edition: Digitalisierte Ausg. Schulze, Ernst August, 1721 - 1786 Dissertatio De Herodiana Puerorum Bethlehemiticorum Caede Francofurti ad Viadrum : Winterus, 1765

Additional Edition: Digitalisierte Ausg. Schulze, Ernst August, 1721 - 1786 Dissertatio De Herodiana Puerorum Bethlehemiticorum Caede Francofurti ad Viadrum : Winterus, 1765

Language: Latin

Keywords: Bibel 1-2 Matthäusevangelium ; Jesus Christus ; Matthäus Evangelist, Heiliger ; Bibel Matthäusevangelium ; Bibel Evangelien ; Bibel Neues Testament ; Theologie ; Exegese ; Bibelwissenschaft ; Kindermord in Bethlehem ; Dissertation:theol.

Author information: Conrad, Christoph Friedrich 1743-1811

Author information: Winter, Johann Christian -1791

Author information: Schulze, Ernst August 1721-1786

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Format: xvii421 Seiten : , Illustrationen, Diagramme.

ISBN: 978-3-030-65320-0

Series Statement: Lecture Notes in Physics Volume 980

Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-030-65321-7

Language: English

Subjects: Physics

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Format: 1 online resource (424 pages).

ISBN: 3-030-65321-8

Series Statement: Lecture Notes in Physics ; 980

Note: Intro -- Preface -- Organization -- Acknowledgements -- References -- Contents -- About the Author -- 1 Introduction -- 1.1 Strings, a Distinguished Theory -- 1.2 String Theory -- 1.2.1 Properties -- Worldsheet CFT -- Spectrum -- 1.2.2 Classification of Superstring Theories -- 1.2.3 Interactions -- Worldsheet and Riemann Surfaces -- Amplitudes -- Divergences and Feynman Graphs -- 1.3 String Field Theory -- 1.3.1 From the Worldsheet to Field Theory -- 1.3.2 String Field Action -- 1.3.3 Expression with Spacetime Fields -- 1.3.4 Applications -- 1.4 Suggested Readings -- References -- Part I Worldsheet Theory -- 2 Worldsheet Path Integral: Vacuum Amplitudes -- 2.1 Worldsheet Action and Symmetries -- 2.2 Path Integral -- 2.3 Faddeev-Popov Gauge Fixing -- 2.3.1 Metrics on Riemann Surfaces -- 2.3.2 Reparametrizations and Analysis of P1 -- Teichmüller Deformations -- Conformal Killing Vectors -- 2.3.3 Weyl Transformations and Quantum Anomalies -- 2.3.4 Ambiguities, Ultralocality and Cosmological Constant -- 2.3.5 Gauge Fixed Path Integral -- 2.4 Ghost Action -- 2.4.1 Actions and Equations of Motion -- 2.4.2 Weyl Ghost -- 2.4.3 Zero-Modes -- 2.5 Normalization -- 2.6 Summary -- 2.7 Suggested Readings -- References -- 3 Worldsheet Path Integral: Scattering Amplitudes -- 3.1 Scattering Amplitudes on Moduli Space -- 3.1.1 Vertex Operators and Path Integral -- 3.1.2 Gauge Fixing: General Case -- 3.1.3 Gauge Fixing: 2-Point Amplitude -- Review of the Problem -- Computation of the Amplitude -- Expression with Ghosts -- 3.2 BRST Quantization -- 3.2.1 BRST Symmetry -- 3.2.2 BRST Cohomology and Physical States -- 3.3 Summary -- 3.4 Suggested Readings -- References -- 4 Worldsheet Path Integral: Complex Coordinates -- 4.1 Geometry of Complex Manifolds -- 4.2 Complex Representation of Path Integral -- 4.3 Summary -- 4.4 Suggested Readings -- References. , 5 Conformal Symmetry in D Dimensions -- 5.1 CFT on a General Manifold -- 5.2 CFT on Minkowski Space -- 5.3 Suggested Readings -- References -- 6 Conformal Field Theory on the Plane -- 6.1 The Riemann Sphere -- 6.1.1 Map to the Complex Plane -- 6.1.2 Relation to the Cylinder: String Theory -- 6.2 Classical CFTs -- 6.2.1 Witt Conformal Algebra -- 6.2.2 PSL(2, C) Conformal Group -- 6.2.3 Definition of a CFT -- 6.3 Quantum CFTs -- 6.3.1 Virasoro Algebra -- 6.3.2 Correlation Functions -- 6.4 Operator Formalism and Radial Quantization -- 6.4.1 Radial Ordering and Commutators -- 6.4.2 Operator Product Expansions -- 6.4.3 Hermitian and BPZ Conjugation -- 6.4.4 Mode Expansion -- 6.4.5 Hilbert Space -- State-Operator Correspondence -- Euclidean and BPZ Conjugations and Inner Products -- Verma Modules -- Normal Ordering -- 6.4.6 CFT on the Cylinder -- 6.5 Suggested Readings -- References -- 7 CFT Systems -- 7.1 Free Scalar -- 7.1.1 Covariant Action -- 7.1.2 Action on the Complex Plane -- 7.1.3 OPE -- 7.1.4 Mode Expansions -- 7.1.5 Commutators -- 7.1.6 Hilbert Space -- 7.1.7 Euclidean and BPZ Conjugates -- 7.2 First-Order bc Ghost System -- 7.2.1 Covariant Action -- 7.2.2 Action on the Complex Plane -- 7.2.3 OPE -- 7.2.4 Mode Expansions -- 7.2.5 Commutators -- 7.2.6 Hilbert Space -- Energy Vacuum (Grassmann Odd) -- Energy Normal Ordering (Grassmann Odd) -- Structure of the Hilbert Space (Grassmann Odd) -- 7.2.7 Euclidean and BPZ Conjugates -- 7.2.8 Summary -- 7.3 Suggested Readings -- References -- 8 BRST Quantization -- 8.1 BRST for Reparametrization Invariance -- 8.2 BRST in the CFT Formalism -- 8.2.1 OPE -- 8.2.2 Mode Expansions -- 8.2.3 Commutators -- 8.3 BRST Cohomology: Two Flat Directions -- 8.3.1 Conditions on the States -- 8.3.2 Relative Cohomology -- Light-Cone Parametrization -- Reduced Cohomology -- Full Relative Cohomology. , 8.3.3 Absolute Cohomology, States and No-Ghost Theorem -- 8.3.4 Cohomology for Holomorphic and Anti-holomorphic Sectors -- 8.4 Summary -- 8.5 Suggested Readings -- References -- Part II String Field Theory -- 9 String Field -- 9.1 Field Functional -- 9.2 Field Expansion -- 9.3 Summary -- 9.4 Suggested Readings -- References -- 10 Free BRST String Field Theory -- 10.1 Classical Action for the Open String -- 10.1.1 Warm-Up: Point-Particle -- 10.1.2 Open String Action -- 10.1.3 Gauge Invariance -- 10.1.4 Siegel Gauge -- 10.2 Open String Field Expansion, Parity and Ghost Number -- 10.3 Path Integral Quantization -- 10.3.1 Tentative Faddeev-Popov Gauge Fixing -- 10.3.2 Tower of Ghosts -- 10.4 Spacetime Action -- 10.5 Closed String -- 10.6 Summary -- 10.7 Suggested Readings -- References -- 11 Introduction to Off-Shell String Theory -- 11.1 Motivations -- 11.1.1 3-Point Function -- 11.1.2 4-Point Function -- 11.2 Off-Shell States -- 11.3 Off-Shell Amplitudes -- 11.3.1 Amplitudes from the Marked Moduli Space -- 11.3.2 Local Coordinates -- 11.4 Suggested Readings -- References -- 12 Geometry of Moduli Spaces and Riemann Surfaces -- 12.1 Parametrization of P(g,n) -- 12.2 Tangent Space -- 12.3 Plumbing Fixture -- 12.3.1 Separating Case -- 12.3.2 Non-separating Case -- 12.3.3 Decomposition of Moduli Spaces and DegenerationLimit -- 12.3.4 Stubs -- 12.4 Summary -- 12.5 Suggested Readings -- References -- 13 Off-Shell Amplitudes -- 13.1 Cotangent Spaces and Amplitudes -- 13.1.1 Construction of Forms -- 13.1.2 Amplitudes and Surface States -- 13.2 Properties of Forms -- 13.2.1 Vanishing of Forms with Trivial Vectors -- 13.2.2 BRST Identity -- 13.3 Properties of Amplitudes -- 13.3.1 Restriction to hat P(g,n) -- 13.3.2 Consequences of the BRST Identity -- 13.4 Suggested Readings -- References -- 14 Amplitude Factorization and Feynman Diagrams. , 14.1 Amplitude Factorization -- 14.1.1 Separating Case -- 14.1.2 Non-separating Case -- 14.2 Feynman Diagrams and Feynman Rules -- 14.2.1 Feynman Graphs -- 14.2.2 Propagator -- 14.2.3 Fundamental Vertices -- Recursive Definition: Tree-Level Vertices -- Recursive Definition: General Vertices -- Other Vertices -- 14.2.4 Stubs -- 14.2.5 1PI Vertices -- 14.3 Properties of Fundamental Vertices -- 14.3.1 String Product -- 14.3.2 Feynman Graph Interpretation -- 14.4 Suggested Readings -- References -- 15 Closed String Field Theory -- 15.1 Closed String Field Expansion -- 15.2 Gauge Fixed Theory -- 15.2.1 Kinetic Term and Propagator -- 15.2.2 Interactions -- 15.2.3 Action -- 15.3 Classical Gauge Invariant Theory -- 15.4 BV Theory -- 15.5 1PI Theory -- 15.6 Suggested Readings -- References -- 16 Background Independence -- 16.1 The Concept of Background Independence -- 16.2 Problem Setup -- 16.3 Deformation of the CFT -- 16.4 Expansion of the Action -- 16.5 Relating the Equations of Motion -- 16.6 Idea of the Proof -- 16.7 Suggested Readings -- References -- 17 Superstring -- 17.1 Worldsheet Superstring Theory -- 17.1.1 Heterotic Worldsheet -- Beta-Gamma System -- 17.1.2 Hilbert Spaces -- 17.2 Off-Shell Superstring Amplitudes -- 17.2.1 Amplitudes -- 17.2.2 Factorization -- 17.2.3 Spurious Poles -- Origin -- Vertical Integration: Large Hilbert Space -- Vertical Integration: Small Hilbert Space -- 17.3 Superstring Field Theory -- 17.3.1 String Field and Propagator -- 17.3.2 Constraint Approach -- 17.3.3 Auxiliary Field Approach -- 17.3.4 Large Hilbert Space -- 17.4 Suggested Readings -- References -- 18 Momentum-Space SFT -- 18.1 General Form -- 18.2 Generalized Wick Rotation -- 18.3 Suggested Readings -- References -- A Conventions -- A.1 Coordinates -- A.2 Operators -- A.3 QFT -- A.4 Curved Space and Gravity -- A.5 List of Symbols. , B Summary of Important Formulas -- B.1 Complex Analysis -- B.2 QFT, Curved Spaces and Gravity -- B.2.1 Two Dimensions -- B.3 Conformal Field Theory -- B.3.1 Complex Plane -- B.3.2 General Properties -- B.3.3 Hermitian and BPZ Conjugations -- Hermitian -- BPZ -- B.3.4 Scalar Field -- B.3.5 Reparametrization Ghosts -- B.4 Bosonic String -- C Quantum Field Theory -- C.1 Path Integrals -- C.1.1 Integration Measure -- C.1.2 Field Redefinitions -- C.1.3 Zero-Modes -- C.2 BRST Quantization -- C.3 BV Formalism -- C.3.1 Properties of Gauge Algebra -- C.3.2 Classical BV -- C.3.3 Quantum BV -- C.4 Suggested Readings -- References -- Index.

Additional Edition: ISBN 3-030-65320-X

Language: English

UID:

Format: XVII, 421 p. 1 illus. , online resource.

Edition: 1st ed. 2021.

ISBN: 9783030653217

Series Statement: Lecture Notes in Physics, 980

Content: This textbook provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far due to the exceptional properties of two-dimensional theories, it becomes cumbersome for some questions or even fails at a more fundamental level. These motivations have led to the development of SFT, a description of string theory using the field theory formalism (second-quantization). As a field theory, SFT provides a rigorous and constructive formulation of string theory. The main focus of the book is the construction of the closed bosonic SFT. The accent is put on providing the reader with the foundations, conceptual understanding and intuition of what SFT is. After reading this book, the reader is able to study the applications from the literature. The book is organized in two parts. The first part reviews the notions of the worldsheet theory that are necessary to build SFT (worldsheet path integral, CFT and BRST quantization). The second part starts by introducing general concepts of SFT from the BRST quantization. Then, it introduces off-shell string amplitudes before providing a Feynman diagrams interpretation from which the building blocks of SFT are extracted. After constructing the closed SFT, the author outlines the proofs of several important properties such as background independence, unitarity and crossing symmetry. Finally, the generalization to the superstring is also discussed.

Note: Introduction -- Worldsheet path integral: vacuum amplitudes -- Worldsheet path integral: scattering amplitudes -- Worldsheet path integral: complex coordinates -- Conformal field theory in D dimensions -- Conformal field theory on the plane -- CFT systems -- BRST quantization -- String field -- Free BRST string field theory -- Introduction to off-shell string theory -- Geometry of moduli spaces and Riemann surfaces -- Off-shell amplitudes.-Amplitude factorization and Feynman diagrams -- Closed string field theory -- Background independence -- Superstring -- Momentum-space SFT.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783030653200

Additional Edition: Printed edition: ISBN 9783030653224

Language: English

DOI: 10.1007/978-3-030-65321-7

URL: https://doi.org/10.1007/978-3-030-65321-7