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Modular Covariance, PCT, Spin and Statistics
 Ann. Inst. Henri Poincare
, 1995
"... . The notion of modular covariance is reviewed and the reconstruction of the Poincar'e group extended to the lowdimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described. Supported in part by MURST and CNRGNAFA. Email: guido@mat.utovrm.it 1 ..."
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Cited by 10 (4 self)
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. The notion of modular covariance is reviewed and the reconstruction of the Poincar'e group extended to the lowdimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described. Supported in part by MURST and CNRGNAFA. Email: guido@mat.utovrm.it 1
Multiinterval subfactors and modularity of representations in conformal field theory
 Commun. Math. Phys
"... Dedicated to John E. Roberts on the occasion of his sixtieth birthday We describe the structure of the inclusions of factors A(E) ⊂A(E ′ ) ′ associated with multiintervals E ⊂ R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. I ..."
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Cited by 112 (37 self)
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is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry.
On the PCTTheorem in the Theory of Local Observables
, 2000
"... We review the PCTtheorem and problems connected with its demonstration. We add a new proof of the PCTtheorem in the theory of local observables which is similar to that one of Jost in Wightman quantum field theory. We also look at consequences in case the PCTsymmetry is given on the algebraic le ..."
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Cited by 5 (0 self)
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We review the PCTtheorem and problems connected with its demonstration. We add a new proof of the PCTtheorem in the theory of local observables which is similar to that one of Jost in Wightman quantum field theory. We also look at consequences in case the PCTsymmetry is given on the algebraic
Modular Structure and Duality in Conformal Quantum Field Theory
 COMMUN.MATH.PHYS
, 1993
"... Making use of a recent result of Borchers, an algebraic version of the BisognanoWichmann theorem is given for conformal quantum field theories, i.e. the TomitaTakesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector concides with the evolution given ..."
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Cited by 77 (29 self)
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cosheaf on the superworld ˜ M, i.e. the universal covering of the DiracWeyl compactification of M. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even spacetime dimension. Analogous results hold for a Poincaré covariant theory provided the modular groups corresponding to wedge algebras
andSpacetimeSymmetryGroups GeometricModularAction
"... Abstract.Aconditionofgeometricmodularactionisproposedasaselection principleforphysicallyinterestingstatesongeneralspacetimes.Thiscondition MartinFlorigandStephenJ.Summers DetlevBuchholz,OlafDreyer, isnaturallyassociatedwithtransformationgroupsofpartiallyorderedsetsand providesthesegroupswithproject ..."
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.Introduction...........................................................................................p.2 II.NetsofOperatorAlgebrasandModularTransformationGroups....p.4 III.GeometricModularActioninQuantumFieldTheory......................p.9.........................................................................................................................p.16 IV.GeometricModular
PCT Symmetry, Dirac Determinant, and Correlation Functions
"... Abstract: We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravityfermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved for ..."
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Abstract: We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravityfermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved
Modular Hecke algebras and their Hopf symmetry
"... We introduce and begin to analyse a class of algebras, associated to congruence subgroups, that extend both the algebra of modular forms of all levels and the ring of classical Hecke operators. At the intuitive level, these are algebras of ‘polynomial coordinates’ for the ‘transverse space’ of latti ..."
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Cited by 40 (10 self)
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We introduce and begin to analyse a class of algebras, associated to congruence subgroups, that extend both the algebra of modular forms of all levels and the ring of classical Hecke operators. At the intuitive level, these are algebras of ‘polynomial coordinates’ for the ‘transverse space
Geometric Modular Action and Spacetime Symmetry Groups
, 1998
"... A condition of geometric modular action is proposed as a selection principle for physically interesting states on general spacetimes. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable ..."
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Cited by 61 (9 self)
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A condition of geometric modular action is proposed as a selection principle for physically interesting states on general spacetimes. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under
Commutation Relations and Modular Symmetries
, 1995
"... Recently Borchers has shown that in a theory of local observables, certain unitary and antiunitary operators, which are obtained from an elementary construction suggested by Bisognano and Wichmann, commute with the translation operators like Lorentz boosts and P1CToperators, respectively. We conclud ..."
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Cited by 9 (4 self)
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conclude from this that as soon as the operators considered implement any symmetry, this symmetry can be fixed up to at most some translation. As a symmetry, we admit any unitary or antiunitary operator under whose adjoint action any algebra of local observables is mapped onto an algebra which can
Modularity and Symmetry in Computational Embryogeny
"... Modularity and symmetry are two properties observed in almost every engineering and biological structure. The origin of these properties in nature is still unknown. Yet, as engineers we tend to generate designs which share these properties. In this paper we will report on the origin of these propert ..."
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Cited by 2 (1 self)
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Modularity and symmetry are two properties observed in almost every engineering and biological structure. The origin of these properties in nature is still unknown. Yet, as engineers we tend to generate designs which share these properties. In this paper we will report on the origin
Results 1  10
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42,249