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Infinite dimensional geometry and quantum field theory of strings. III. Infinite dimensional W-geometry of a second quantized free string | | D.Juriev
; | | Date: |
7 Dec 1993 | | Journal: | J.Geom.Phys. 16 (1995) 275-300 | | Subject: | High Energy Physics - Theory; Algebraic Geometry; Functional Analysis | hep-th alg-geom funct-an math.AG math.FA | | Abstract: | The present paper is devoted to various objects of the infinite dimensional W-geometry of a second quantized free string. Our purpose is to include the W-symmetries into the general infinite dimensional geometrical picture related to the quantum field theory of strings, which was described in the first part of the paper (Algebras Groups Geom.11(1994)[to appear]). It is done by the change of the Lie algebra of all infinitesimal reparametrizations of a string world-sheet on the Lie quasi(pseudo)algebra of classical W-transformations (Gervais-Matsuo quasi(pseudo)algebra) as well as of the Virasoro algebra on the central extended enlarged Gervais-Matsuo quasi(pseudo)algebra. A way to obtain W-algebras from classical W-transformations (i.e. Gervais-Matsuo quasi (pseudo)algebra) is proposed. The relation of Gervais-Matsuo differential W-geometry to the Batalin-Weinstein-Karasev-Maslov approach to nonlinear Poisson brackets as well as to L.V.Sabinin program of "nonlinear geometric algebra" are mentioned. | | Source: | arXiv, hep-th/9401026 | | Services: | Forum | Review | PDF | Favorites | |
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