Two-Dimensional Conformal Geometry and Vertex Operator Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1997
|
| Schriftenreihe: | Progress in Mathematics
148 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical structures of conformal field theories. Much of the recent progress has deep connections with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in [Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Virasoro and affine KacMoody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on. He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a "big and important problem. " On the one hand, the theory of vertex operator algebras and their representations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions |
| Beschreibung: | 1 Online-Ressource (XIV, 282 p) |
| ISBN: | 9781461242765 9781461287209 |
| DOI: | 10.1007/978-1-4612-4276-5 |
Internformat
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| 500 | |a The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical structures of conformal field theories. Much of the recent progress has deep connections with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in [Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Virasoro and affine KacMoody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on. He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a "big and important problem. " On the one hand, the theory of vertex operator algebras and their representations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions | ||
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Datensatz im Suchindex
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| author | Huang, Yi-Zhi |
| author_facet | Huang, Yi-Zhi |
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| author_sort | Huang, Yi-Zhi |
| author_variant | y z h yzh |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4276-5 |
| format | Electronic eBook |
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| id | DE-604.BV042420262 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461242765 9781461287209 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855679 |
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| physical | 1 Online-Ressource (XIV, 282 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
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| publisher | Birkhäuser Boston |
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| series | Progress in Mathematics |
| series2 | Progress in Mathematics |
| spelling | Huang, Yi-Zhi Verfasser aut Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang Boston, MA Birkhäuser Boston 1997 1 Online-Ressource (XIV, 282 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 148 The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical structures of conformal field theories. Much of the recent progress has deep connections with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in [Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Virasoro and affine KacMoody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on. He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a "big and important problem. " On the one hand, the theory of vertex operator algebras and their representations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions Mathematics Algebra Geometry, algebraic Topological Groups Operator theory Geometry Mathematical physics Algebraic Geometry Operator Theory Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Vertexalgebra (DE-588)4328736-0 gnd rswk-swf Konforme Differentialgeometrie (DE-588)4206468-5 gnd rswk-swf Konforme Feldtheorie (DE-588)4312574-8 gnd rswk-swf Vertexoperator (DE-588)4188067-5 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Vertexoperator (DE-588)4188067-5 s Vertexalgebra (DE-588)4328736-0 s Konforme Differentialgeometrie (DE-588)4206468-5 s Konforme Feldtheorie (DE-588)4312574-8 s Dimension 2 (DE-588)4321721-7 s 1\p DE-604 Progress in Mathematics 148 (DE-604)BV000004120 148 https://doi.org/10.1007/978-1-4612-4276-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Huang, Yi-Zhi Two-Dimensional Conformal Geometry and Vertex Operator Algebras Progress in Mathematics Mathematics Algebra Geometry, algebraic Topological Groups Operator theory Geometry Mathematical physics Algebraic Geometry Operator Theory Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Vertexalgebra (DE-588)4328736-0 gnd Konforme Differentialgeometrie (DE-588)4206468-5 gnd Konforme Feldtheorie (DE-588)4312574-8 gnd Vertexoperator (DE-588)4188067-5 gnd Dimension 2 (DE-588)4321721-7 gnd |
| subject_GND | (DE-588)4328736-0 (DE-588)4206468-5 (DE-588)4312574-8 (DE-588)4188067-5 (DE-588)4321721-7 |
| title | Two-Dimensional Conformal Geometry and Vertex Operator Algebras |
| title_auth | Two-Dimensional Conformal Geometry and Vertex Operator Algebras |
| title_exact_search | Two-Dimensional Conformal Geometry and Vertex Operator Algebras |
| title_full | Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang |
| title_fullStr | Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang |
| title_full_unstemmed | Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang |
| title_short | Two-Dimensional Conformal Geometry and Vertex Operator Algebras |
| title_sort | two dimensional conformal geometry and vertex operator algebras |
| topic | Mathematics Algebra Geometry, algebraic Topological Groups Operator theory Geometry Mathematical physics Algebraic Geometry Operator Theory Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Vertexalgebra (DE-588)4328736-0 gnd Konforme Differentialgeometrie (DE-588)4206468-5 gnd Konforme Feldtheorie (DE-588)4312574-8 gnd Vertexoperator (DE-588)4188067-5 gnd Dimension 2 (DE-588)4321721-7 gnd |
| topic_facet | Mathematics Algebra Geometry, algebraic Topological Groups Operator theory Geometry Mathematical physics Algebraic Geometry Operator Theory Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Vertexalgebra Konforme Differentialgeometrie Konforme Feldtheorie Vertexoperator Dimension 2 |
| url | https://doi.org/10.1007/978-1-4612-4276-5 |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT huangyizhi twodimensionalconformalgeometryandvertexoperatoralgebras |