Geodesic
Rigorous Formulation of a $2D$ Conformal Model in the Fock–Krein Space: Construction of the Global $\operatorname{Op}J^*$-Algebra of Fields and Currents
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 1, pp. 60-79 Cet article a éte moissonné depuis la source Math-Net.Ru

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We use the formalism of the $2D$ massless scalar field model in an indefinite space of the Fock–Krein type as a basis for constructing a rigorous formulation of $2D$ quantum conformal theories. We show that the sought construction is a several-stage procedure whose central block is the construction of a new type of representation of the Virasoro algebra. We develop the first stage of this procedure, which is to construct a special global algebra of fields and currents generated by exponential generators. We obtain a system of commutation relations for the Wick-squared currents used in the definition of the Virasoro generators. We prove the existence of Wick exponentials of the current given by operator-valued generalized functions; the sought global algebra is rigorously defined as the algebra of current and field, Wick and normal exponentials on a common dense invariant domain in a Fock–Krein space.
Keywords: Fock–Krein space, conformal theory, field algebra. 
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     author = {S. S. Horuzhy},
     title = {Rigorous {Formulation} of a $2D$ {Conformal} {Model} in the {Fock{\textendash}Krein} {Space:} {Construction} of the {Global} $\operatorname{Op}J^*${-Algebra} of {Fields} and {Currents}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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S. S. Horuzhy. Rigorous Formulation of a $2D$ Conformal Model in the Fock–Krein Space: Construction of the Global $\operatorname{Op}J^*$-Algebra of Fields and Currents. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 1, pp. 60-79. http://geodesic.mathdoc.fr/item/TMF_2004_141_1_a3/

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