Riemann surfaces, Clifford algebras and infinite dimensional groups
We introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a "gauge" group of meromorphic functions on the Riemann...
| Main Authors: | , , |
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
Springer-Verlag
1990
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| _version_ | 1826290126589788160 |
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| author | Carey, A Eastwood, MG Hannabuss, K |
| author_facet | Carey, A Eastwood, MG Hannabuss, K |
| author_sort | Carey, A |
| collection | OXFORD |
| description | We introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a "gauge" group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. © 1990 Springer-Verlag. |
| first_indexed | 2024-03-07T02:39:25Z |
| format | Journal article |
| id | oxford-uuid:a9ebe6d1-368a-484a-b19c-dece0d416657 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:39:25Z |
| publishDate | 1990 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | oxford-uuid:a9ebe6d1-368a-484a-b19c-dece0d4166572022-03-27T03:11:44ZRiemann surfaces, Clifford algebras and infinite dimensional groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a9ebe6d1-368a-484a-b19c-dece0d416657EnglishSymplectic Elements at OxfordSpringer-Verlag1990Carey, AEastwood, MGHannabuss, KWe introduce a class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a "gauge" group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. © 1990 Springer-Verlag. |
| spellingShingle | Carey, A Eastwood, MG Hannabuss, K Riemann surfaces, Clifford algebras and infinite dimensional groups |
| title | Riemann surfaces, Clifford algebras and infinite dimensional groups |
| title_full | Riemann surfaces, Clifford algebras and infinite dimensional groups |
| title_fullStr | Riemann surfaces, Clifford algebras and infinite dimensional groups |
| title_full_unstemmed | Riemann surfaces, Clifford algebras and infinite dimensional groups |
| title_short | Riemann surfaces, Clifford algebras and infinite dimensional groups |
| title_sort | riemann surfaces clifford algebras and infinite dimensional groups |
| work_keys_str_mv | AT careya riemannsurfacescliffordalgebrasandinfinitedimensionalgroups AT eastwoodmg riemannsurfacescliffordalgebrasandinfinitedimensionalgroups AT hannabussk riemannsurfacescliffordalgebrasandinfinitedimensionalgroups |