A Quantization Procedure of Fields Based on Geometric Langlands Correspondence
We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group GL. Use the sigma m...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/749631 |
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| _version_ | 1841524655305785344 |
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| author | Do Ngoc Diep |
| author_facet | Do Ngoc Diep |
| author_sort | Do Ngoc Diep |
| collection | DOAJ |
| description | We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group GL. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundles with connection over the space dual to the Lie algebra of the symmetry group GL. After that we quantize the vector bundles with connection over the coadjoint orbits of the symmetry group GL. Use the electric-magnetic duality to pass to the Langlands dual Lie group G. Therefore, we have some affine Kac-Moody loop algebra of meromorphic functions with values in Lie algebra =Lie(G). Use the construction of Fock space reprsentations to have representations of such affine loop algebra. And finally, we have the automorphic
representations of the corresponding Langlands-dual Lie groups G. |
| format | Article |
| id | doaj-art-abb5f52b43dd4c31b55f234954a46da9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-abb5f52b43dd4c31b55f234954a46da92025-02-03T05:47:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/749631749631A Quantization Procedure of Fields Based on Geometric Langlands CorrespondenceDo Ngoc Diep0Department of Geometry and Topology, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road Cau Giay District 10307, Hanoi, VietnamWe expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group GL. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundles with connection over the space dual to the Lie algebra of the symmetry group GL. After that we quantize the vector bundles with connection over the coadjoint orbits of the symmetry group GL. Use the electric-magnetic duality to pass to the Langlands dual Lie group G. Therefore, we have some affine Kac-Moody loop algebra of meromorphic functions with values in Lie algebra =Lie(G). Use the construction of Fock space reprsentations to have representations of such affine loop algebra. And finally, we have the automorphic representations of the corresponding Langlands-dual Lie groups G.http://dx.doi.org/10.1155/2009/749631 |
| spellingShingle | Do Ngoc Diep A Quantization Procedure of Fields Based on Geometric Langlands Correspondence International Journal of Mathematics and Mathematical Sciences |
| title | A Quantization Procedure of Fields Based on Geometric Langlands Correspondence |
| title_full | A Quantization Procedure of Fields Based on Geometric Langlands Correspondence |
| title_fullStr | A Quantization Procedure of Fields Based on Geometric Langlands Correspondence |
| title_full_unstemmed | A Quantization Procedure of Fields Based on Geometric Langlands Correspondence |
| title_short | A Quantization Procedure of Fields Based on Geometric Langlands Correspondence |
| title_sort | quantization procedure of fields based on geometric langlands correspondence |
| url | http://dx.doi.org/10.1155/2009/749631 |
| work_keys_str_mv | AT dongocdiep aquantizationprocedureoffieldsbasedongeometriclanglandscorrespondence AT dongocdiep quantizationprocedureoffieldsbasedongeometriclanglandscorrespondence |