Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories. i.e the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector coincides with the evolution given by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space M, and Haag duality for double cones holds provided the net of local algebras is extended to a pre-cosheaf on the superworld M, i.e. the universal covering of the Dirac-Weyl compactification of M. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even space-time dimension. Analogous results hold for a Poincare covariant theory provided the modular groups corresponding to wedge algebras have the expected geometrical meaning and the split property is satisfied. In particular the Poincare representation is unique in this case.

Brunetti, R., Guido, D., & Longo, R. (1993). Modular structure and duality in conformal quantum field theory. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 156(1), 201-219 [10.1007/BF02096738].

Modular structure and duality in conformal quantum field theory

GUIDO, DANIELE;LONGO, ROBERTO
1993

Abstract

Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories. i.e the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector coincides with the evolution given by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space M, and Haag duality for double cones holds provided the net of local algebras is extended to a pre-cosheaf on the superworld M, i.e. the universal covering of the Dirac-Weyl compactification of M. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even space-time dimension. Analogous results hold for a Poincare covariant theory provided the modular groups corresponding to wedge algebras have the expected geometrical meaning and the split property is satisfied. In particular the Poincare representation is unique in this case.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - Analisi Matematica
eng
Con Impact Factor ISI
wedge region; algebraic version of the Bisognano-Wichmann theorem; conformal quantum field theories; Tomita-Takesaki modular group; von Neumann algebra of a wedge region; vacuum vector; Lorentz transformations; essential duality; pre-cosheaf; Dirac-Weyl compactification; PCT symmetry; Poincaré covariant theory; modular groups; Poincaré representation
Brunetti, R., Guido, D., & Longo, R. (1993). Modular structure and duality in conformal quantum field theory. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 156(1), 201-219 [10.1007/BF02096738].
Brunetti, R; Guido, D; Longo, R
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/43492
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