1,166 research outputs found
Covariant Sectors with Infinite Dimension and Positivity of the Energy
We consider a Moebius covariant sector, possibly with infinite dimension, of
a local conformal net of von Neumann algebras on the circle. If the sector has
finite index, it has automatically positive energy. In the infinite index case,
we show the spectrum of the energy always to contain the positive real line,
but, as seen by an example, it may contain negative values. We then consider
nets with Haag duality on the real line, or equivalently sectors with
non-solitonic extension to the dual net; we give a criterion for irreducible
sectors to have positive energy, namely this is the case iff there exists an
unbounded Moebius covariant left inverse. As a consequence the class of sectors
with positive energy is stable under composition, conjugation and direct
integral decomposition.Comment: 25 pages, Latex2
On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity
We first give an overview of the basic theory for discrete unital twisted
C*-dynamical systems and their covariant representations on Hilbert C*-modules.
After introducing the notion of equivariant representations of such systems and
their product with covariant representations, we prove a kind of Fell
absorption principle saying that the product of an induced regular equivariant
representation with a covariant faithful representation is weakly equivalent to
an induced regular covariant representation. This principle is the key to our
main result, namely that a certain property, formally weaker than Exel's
approximation property, ensures that the system is regular, i.e., the
associated full and reduced C*-crossed products are canonically isomorphic.Comment: Final version, to appear in Muenster J. Math. A permanence result for
the weak approximation property, some corollaries of it and two examples have
been added to Section 5. Some side results in Section 4 have been removed and
will be included in a subsequent paper. The Introduction has also been partly
rewritte
Classification of Subsystems for Local Nets with Trivial Superselection Structure
Let F be a local net of von Neumann algebras in four spacetime dimensions
satisfying certain natural structural assumptions. We prove that if F has
trivial superselection structure then every covariant, Haag-dual subsystem B is
the fixed point net under a compact group action on one component in a suitable
tensor product decomposition of F. Then we discuss some application of our
result, including free field models and certain theories with at most countably
many sectors.Comment: 31 pages, LaTe
Labeled Trees and Localized Automorphisms of the Cuntz Algebras
We initiate a detailed and systematic study of automorphisms of the Cuntz
algebras \O_n which preserve both the diagonal and the core -subalgebra.
A general criterion of invertibility of endomorphisms yielding such
automorphisms is given. Combinatorial investigations of endomorphisms related
to permutation matrices are presented. Key objects entering this analysis are
labeled rooted trees equipped with additional data. Our analysis provides
insight into the structure of {\rm Aut}(\O_n) and leads to numerous new
examples. In particular, we completely classify all such automorphisms of
for the permutation unitaries in . We show that
the subgroup of {\rm Out}(\O_2) generated by these automorphisms contains a
copy of the infinite dihedral group .Comment: 35 pages, slight changes, to appear on Trans. Amer. Math. So
Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models
We introduced in a previous paper a general notion of asymptotic morphism of
a given local net of observables, which allows to describe the sectors of a
corresponding scaling limit net. Here, as an application, we illustrate the
general framework by analyzing the Schwinger model, which features confined
charges. In particular, we explicitly construct asymptotic morphisms for these
sectors in restriction to the subnet generated by the derivatives of the field
and momentum at time zero. As a consequence, the confined charges of the
Schwinger model are in principle accessible to observation. We also study the
obstructions, that can be traced back to the infrared singular nature of the
massless free field in d=2, to perform the same construction for the complete
Schwinger model net. Finally, we exhibit asymptotic morphisms for the net
generated by the massive free charged scalar field in four dimensions, where no
infrared problems appear in the scaling limit.Comment: 36 pages; no figure
The Fourier–Stieltjes algebra of a C*-dynamical system
In analogy with the Fourier–Stieltjes algebra of a group, we associate to a unital discrete
twisted C∗-dynamical system a Banach algebra whose elements are coefficients of
equivariant representations of the system. Building upon our previous work, we show
that this Fourier–Stieltjes algebra embeds continuously in the Banach algebra of completely
bounded multipliers of the (reduced or full) C∗-crossed product of the system.
We introduce a notion of positive definiteness and prove a Gelfand–Raikov type theorem
allowing us to describe the Fourier–Stieltjes algebra of a system in a more intrinsic way.
We also propose a definition of amenability for C∗-dynamical systems and show that it
implies regularity. After a study of some natural commutative subalgebras, we end with
a characterization of the Fourier–Stieltjes algebra involving C∗-correspondences over the
(reduced or full) C∗-crossed product
The Fourier-Stieltjes algebra of a C*-dynamical system
In analogy with the Fourier-Stieltjes algebra of a group, we associate to a
unital discrete twisted C*-dynamical system a Banach algebra whose elements are
coefficients of equivariants representations of the system. Building upon our
previous work, we show that this Fourier-Stieltjes algebra embeds continuously
in the Banach algebra of completely bounded multipliers of the (reduced or
full) C*-crossed product of the system. We also introduce a notion of positive
definiteness and prove a Gelfand-Raikov type theorem allowing us to describe
the Fourier-Stieltjes algebra of a system in a more intrinsic way. After a
study of some of its natural commutative subalgebras, we end with a
characterization of the Fourier-Stieltjes algebra involving C*-correspondences
over the (reduced or full) C*-crossed product.Comment: 46 pages. Minor revision. A few typos were corrected. The proof that
amenability of a system implies its regularity has been streamlined. To
appear in Internat. J. Mat
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