Superselection Theory for Subsystems

Conti, Roberto; Doplicher, Sergio; Roberts, John Η.

doi:10.1007/s002200100392

Cited by 20 publications

(61 citation statements)

References 19 publications

(28 reference statements)

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“…Due to the triviality of the monodromy (which is automatic in four spacetime dimensions) one can use the arguments in [11,12] (see also [9,Sect. 2] for an overview) to get the desired structure on α ∆ .…”

Section: Theorem 35 a Local Extension B Of A (Vir1) Is Of Compact mentioning

confidence: 99%

On the Representation Theory of Virasoro Nets

Carpi

2004

Communications in Mathematical Physics

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We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local extensions of the c = 1 Virasoro net for which the restriction of the vacuum representation to the Virasoro subnet is a direct sum of irreducible subrepresentations with finite statistical dimension (local extensions of compact type). Moreover we prove that if the central charge c is in a certain subset of (1, ∞), including [2, ∞), and h ≥ (c − 1)/24, the irreducible representation with lowest weight h of the corresponding Virasoro net has infinite statistical dimension. As a consequence we show that if the central charge c is in the above set and satisfies c ≤ 25 then the corresponding Virasoro net has no proper local extensions of compact type.

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Section: Theorem 35 a Local Extension B Of A (Vir1) Is Of Compact mentioning

confidence: 99%

On the Representation Theory of Virasoro Nets

Carpi

2004

Communications in Mathematical Physics

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“…For what concerns assumption (i), the Reeh-Schlieder property in the scaling limit can be deduced for the algebras B 0,ι (W ) associated to wedges. Finally, theorem 4.7 of [12] allows to deduce property (v) for F(B 0,ι ) from the absence of sectors with infinite statistics for B 0,ι , however it is not clear how to obtain the latter property from the properties of B.…”

Section: Field Nets With Trivial Superselection Structure In the Scalmentioning

confidence: 99%

“…It has been very successful in the mathematical description of superselection sectors and of the global gauge group of a given QFT [17]. Also, the mathematical tools that are available in this setting are well suited for providing a detailed analysis of subsystems, an issue that is central in order to obtain an intrinsic description of the observable system one starts with [12,10,11]. In another direction, the recently proposed algebraic approach to the renormalization group [8] (see also section 2) has opened the possibility of studying the short distance limit in the local quantum physics framework, and has started to convey new insight into our understanding of physically relevant issues such as confinement of colour charges and renormalization of pointlike fields [3,14,1].…”

Section: Introductionmentioning

confidence: 99%

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Scaling Limit for Subsystems and Doplicher–Roberts Reconstruction

Conti

Morsella

2009

Ann. Henri Poincaré

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Given an inclusion B ⊂ F of (graded) local nets, we analyse the structure of the corresponding inclusion of scaling limit nets B 0 ⊂ F 0 , giving conditions, fulfilled in free field theory, under which the unicity of the scaling limit of F implies that of the scaling limit of B. As a byproduct, we compute explicitly the (unique) scaling limit of the fixpoint nets of scalar free field theories. In the particular case of an inclusion A ⊂ B of local nets with the same canonical field net F, we find sufficient conditions which entail the equality of the canonical field nets of A 0 and B 0 .

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“…As in [10] we will repeatedly exploit the possibility of comparing such constructions for different subsystems given by the functorial properties of the correspondence B → (F B , G B ) discussed in [14].…”

Section: Introductionmentioning

confidence: 99%

Classification of Subsystems for Graded-Local Nets with Trivial Superselection Structure

Carpi

Conti

2004

Commun. Math. Phys.

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We classify Haag-dual Poincaré covariant subsystems B ⊂ F of a graded-local net F on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical field net F A of a net A of local observables satisfying natural assumptions. As a consequence, provided that it has no nontrivial internal symmetries, such an observable net A is generated by (the abstract versions of) the local energy-momentum tensor density and the observable local gauge currents which appear in the algebraic formulation of the quantum Noether theorem. Moreover, for a net A of local observables as above, we also classify the Poincaré covariant local extensions B ⊃ A which preserve the dynamics.

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Superselection Theory for Subsystems

Cited by 20 publications

References 19 publications

On the Representation Theory of Virasoro Nets

On the Representation Theory of Virasoro Nets

Scaling Limit for Subsystems and Doplicher–Roberts Reconstruction

Classification of Subsystems for Graded-Local Nets with Trivial Superselection Structure

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