39,230 research outputs found
Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality
We show that the discrete principal nets in quadrics of constant curvature
that have constant mixed area mean curvature can be characterized by the
existence of a K\"onigs dual in a concentric quadric.Comment: 12 pages, 10 figures, pdfLaTeX (plain pdfTeX source included as bak
file
Ground state representations of loop algebras
Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in
S^1 and identifying the real line with the punctured circle, we consider the
subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the
translation-invariant 2-cocycles on Sg. We show that the ground state
representation of Sg is unique for each cocycle. These ground states correspond
precisely to the vacuum representations of Lg.Comment: 22 pages, no figur
An algebraic Haag's theorem
Under natural conditions (such as split property and geometric modular action
of wedge algebras) it is shown that the unitary equivalence class of the net of
local (von Neumann) algebras in the vacuum sector associated to double cones
with bases on a fixed space-like hyperplane completely determines an algebraic
QFT model. More precisely, if for two models there is unitary connecting all of
these algebras, then --- without assuming that this unitary also connects their
respective vacuum states or spacetime symmetry representations --- it follows
that the two models are equivalent. This result might be viewed as an algebraic
version of the celebrated theorem of Rudolf Haag about problems regarding the
so-called "interaction-picture" in QFT.
Original motivation of the author for finding such an algebraic version came
from conformal chiral QFT. Both the chiral case as well as a related conjecture
about standard half-sided modular inclusions will be also discussed
Automating the transformation-based analysis of visual languages
The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)
Solitons and nonsmooth diffeomorphisms in conformal nets
We show that any solitonic representation of a conformal (diffeomorphism
covariant) net on S^1 has positive energy and construct an uncountable family
of mutually inequivalent solitonic representations of any conformal net, using
nonsmooth diffeomorphisms. On the loop group nets, we show that these
representations induce representations of the subgroup of loops compactly
supported in S^1 \ {-1} which do not extend to the whole loop group.
In the case of the U(1)-current net, we extend the diffeomorphism covariance
to the Sobolev diffeomorphisms D^s(S^1), s > 2, and show that the
positive-energy vacuum representations of Diff_+(S^1) with integer central
charges extend to D^s(S^1). The solitonic representations constructed above for
the U(1)-current net and for Virasoro nets with integral central charge are
continuously covariant with respect to the stabilizer subgroup of Diff_+(S^1)
of -1 of the circle.Comment: 33 pages, 3 TikZ figure
Super-KMS functionals for graded-local conformal nets
Motivated by a few preceding papers and a question of R. Longo, we introduce
super-KMS functionals for graded translation-covariant nets over R with
superderivations, roughly speaking as a certain supersymmetric modification of
classical KMS states on translation-covariant nets over R, fundamental objects
in chiral algebraic quantum field theory. Although we are able to make a few
statements concerning their general structure, most properties will be studied
in the setting of specific graded-local (super-) conformal models. In
particular, we provide a constructive existence and partial uniqueness proof of
super-KMS functionals for the supersymmetric free field, for certain subnets,
and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a
separate result, we classify bounded super-KMS functionals for graded-local
conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare
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