53,737 research outputs found
Rigidity results for Bernoulli actions and their von Neumann algebras (after Sorin Popa)
We survey Sorin Popa's recent work on Bernoulli actions. The paper was
written on the occasion of the Bourbaki seminar. Using very original methods
from operator algebras, Sorin Popa has shown that the orbit structure of the
Bernoulli action of a property (T) group, completely remembers the group and
the action. This information is even essentially contained in the crossed
product von Neumann algebra, yielding the first von Neumann strong rigidity
theorem in the literature. The same methods allow Popa to obtain II_1 factors
with prescribed countable fundamental group.Comment: Minor correction
Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants
Braided subfactors of von Neumann algebras provide a framework for studying
two dimensional conformal field theories and their modular invariants. We
review this in the context of SU(3) conformal field theories through
corresponding SU(3) braided subfactors and various subfactor invariants
including spectral measures for the nimrep graphs, A_2-planar algebras and
almost Calabi-Yau algebras.Comment: 45 pages, 25 figures. v3: minor correction to Figure 14; v2: figures
of 0-1 parts of graphs included, some minor correction
Generic Bell correlation between arbitrary local algebras in quantum field theory
We prove that for any two commuting von Neumann algebras of infinite type,
the open set of Bell correlated states for the two algebras is norm dense. We
then apply this result to algebraic quantum field theory -- where all local
algebras are of infinite type -- in order to show that for any two spacelike
separated regions, there is an open dense set of field states that dictate Bell
correlations between the regions. We also show that any vector state cyclic for
one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e.,
nonseparable) across the algebras -- from which it follows that every field
state with bounded energy is entangled across any two spacelike separated
regions.Comment: Third version; correction in the proof of Proposition
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