Abstract
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.
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Communicated by H. Araki
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Carey, A.L., Eastwood, M.G. & Hannabuss, K.C. Riemann surfaces, Clifford algebras and infinite dimensional groups. Commun.Math. Phys. 130, 217–236 (1990). https://doi.org/10.1007/BF02473351
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DOI: https://doi.org/10.1007/BF02473351