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TMF, 2004, Volume 141, Number 1, Pages 60–79 (Mi tmf114)  

Rigorous Formulation of a $2D$ Conformal Model in the Fock–Krein Space: Construction of the Global $\operatorname{Op}J^*$-Algebra of Fields and Currents

S. S. Horuzhy

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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

DOI: https://doi.org/10.4213/tmf114

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English version:
Theoretical and Mathematical Physics, 2004, 141:1, 1381–1397

Bibliographic databases:

Received: 13.11.2003
Revised: 18.03.2004

Citation: 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”, TMF, 141:1 (2004), 60–79; Theoret. and Math. Phys., 141:1 (2004), 1381–1397

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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