Generalized states in SFT
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The search for analytic solutions in open string fields theory à la Witten often meets with singular expressions, which need an adequate mathematical formalism to be interpreted. In this paper we discuss this problem and propose a way to resolve the related ambiguities. Our claim is that a correct interpretation requires a formalism similar to distribution theory in functional analysis. To this end we concretely construct a locally convex space of test string states together with the dual space of functionals. We show that the above suspicious expressions can be identified with well defined elements of the dual.
KeywordsDual Space Topological Vector Space Strong Topology Normed Vector Space Linear Continuous Functional
L.B. would like to thank Gianni Dal Maso for sharing with him his expertise on functional analysis. We would like to thank D.D. Tolla for discussions and for our using material from previous joint papers. The work of L.B. and S.G. was supported in part by the MIUR-PRIN contract 2009-KHZKRX.
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