Abstract
We present a construction of the closed string algebra in terms of Gaussian processes and crossed products. Also we give a purely functional analytical prove of the sh-Lie-structure.
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[S-Z] Saadi, M., Zwiebach, B.: Closed string field theory from polyhedra. Ann. Phys.192, 213 (1989)
[K] Kak, M.: Geometric derivation of string field theory from first principles: Closed strings and modular invariance. Phys. Rev.D38, 3052 (1988)
[K-K-S] Kugo, T., Kunimoto, H., Suehira, K.: Non-polynomial closed string field theory. Phys. Lett.226B, 48 (1989)
[S] Sen, A.: On the background independence of string field theory. Preprint TIFR/TH/90-7
[St1] Stasheff, J.: An almost groupoid structure for the space of (open) strings and implications for string field theory. In: Advances in Homotopy Theory, LMS Lecture Note Series139, 165 (1989)
[St2] Stasheff, J.: Towards a closed string field theory: Topology and convolution algebra. Preprint UNC-MATH-90/1
[Co-La] Collela, P., Lanford, O.: Sample field behavior for the free markov random field. In: Constructive quantum field theory. Velo, G., Wightman, A. (eds.). Lecture Notes in Physics Vol.25, Berlin, Heidelberg, New York: Springer 1973
[R-SIV] Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. IV, New York: Academic Press 1979
[G-R-S] Guerra, F., Rosen, L., Simon, B.: Boundary conditions inP(Φ) 2 Euclidean field theory. Ann. l'Inst. H. Poincaré115, 231 (1976)
[Si] Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979
[Se] Segal, G.: Unitary representation of some infinite dimensional groups. Commun. Math. Phys.80, 301 (1981)
[Pr-Se] Pressley, A., Segal, G.: Loop groups. Oxford: Clarendon Press 1986
[Mic] Mickelsson, J.: String Quantization on Group Manifolds and the Holomorphic Geometry of DiffS 1/S 1. Commun. Math. Phys.112, 653 (1987)
[Wie1] Wiesbrock, H.-W.: TheC *-algebra of Bosonic Strings. Commun. Math. Phys.136, 369–397 (1991)
[Wie2] Wiesbrock, H.-W.: A Note on the construction of theC *-algebra of Bosonic strings. To be published in J. Math. Phys.
[Pi] Pickrell, D.: Measures on infinite dimensional Grassmann Manifolds. J. Funct. Anal.70, 357 (1987)
[Pen] Penrose, R.: The twistor programme. Rep. Math. Phys.12, 65 (1977)
[F-G-Z] Frenkel, I., Garland, H., Zuckerman, G.: Serni-infinite dimensional cohomology and string theory. Proc. Nat. Acad. Sci. USA83, 844 (1986)
[Mil] Milnor, J.: Remarks on infinite dimensional Lie-groups. In: Relativity, groups and topology II. Les Houches Session XL, de Witt, B., Stora, R. (eds.). (1983)
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Communicated by N. Yu. Reshetikhin
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Wiesbrock, HW. The construction of the sh-Lie-algebra of closed bosonic strings. Commun.Math. Phys. 145, 17–42 (1992). https://doi.org/10.1007/BF02099279
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DOI: https://doi.org/10.1007/BF02099279