544 research outputs found
On Pythagoras' theorem for products of spectral triples
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual
Pythagoras theorem can be formulated in terms of Connes' distance, between pure
states, in the product of commutative spectral triples. We investigate the
generalization to both non pure states and arbitrary spectral triples. We show
that Pythagoras theorem is replaced by some Pythagoras inequalities, that we
prove for the product of arbitrary (i.e. non-necessarily commutative) spectral
triples, assuming only some unitality condition. We show that these
inequalities are optimal, and provide non-unital counter-examples inspired by
K-homology.Comment: Paper slightly shortened to match the published version; Lett. Math.
Phys. 201
Aspirin and the risk of colorectal and other digestive tract cancers: an updated meta-analysis through 2019
Aspirin has been associated with a reduced risk of colorectal cancer, and possibly of a few other digestive tract cancers. The quantification of risk reduction and the optimal dose and duration of aspirin use for the prevention of colorectal and other digestive tract cancers remains unclear
De Sitter Thermodynamics from Diamonds's Temperature
The thermal time hypothesis proposed by Rovelli [1] regards the physical
basis for the flow of time as thermodynamical and provides a definition of the
temperature for some special cases. We verify this hypothesis in the case of de
Sitter spacetime by relating the uniformly accelerated observer in de Sitter
spacetime to the diamond in Minkowski spacetime. Then, as an application of it,
we investigate the thermal effect for the uniformly accelerated observer with a
finite lifetime in dS spacetime, which generalizes the corresponding result for
the case of Minkowski spacetime [2].
Furthermore, noticing that a uniformly accelerated dS observer with a finite
lifetime corresponds to a Rindler observer with a finite lifetime in the
embedding Minkowski spacetime, we show that the
global-embedding-Minkowski-spacetime (GEMS) picture of spacetime thermodynamics
is valid in this case. This is a rather nontrivial and unexpected
generalization of the GEMS picture, as well as a further verification of both
the thermal time hypothesis and the GEMS picture.Comment: 10 pages, 3 figures, LaTeX; v2: reorganized with a new section added
concerning a generalization of the GEMS picture from our result; v3: version
with minor corrections, to appear in JHE
An algebraic Birkhoff decomposition for the continuous renormalization group
This paper aims at presenting the first steps towards a formulation of the
Exact Renormalization Group Equation in the Hopf algebra setting of Connes and
Kreimer. It mostly deals with some algebraic preliminaries allowing to
formulate perturbative renormalization within the theory of differential
equations. The relation between renormalization, formulated as a change of
boundary condition for a differential equation, and an algebraic Birkhoff
decomposition for rooted trees is explicited
mycosis fungoides in childhood description and study of two siblings
Primary cutaneous T-cell lymphomas are exceedingly rare in children and adolescents. However, mycosis fungoides (MF) is the most frequent primary cutaneous lymphoma diagnosed in childhood. Two cases of MF in siblings (a 14-year-old boy and his 10-year-old sister) are reported. On the basis of clinical features (histopathological and immunophenotypical findings) a diagnosis of MF patch lesions was made in both siblings. Since recent data in the literature have underlined a high frequency of the HLA-DQB1*03 allele in patients with familial MF (including child patients), the HLA profile of the patients was analysed, indicating the presence of a haplotype (HLA-DQB1*03,*03 in the girl, HLA-DQB1*02,*03 in the boy) corresponding with that described in recent literature. Two rare and exceptional cases of MF in siblings are reported, highlighting the presence of a peculiar haplotype
Minimal length in quantum space and integrations of the line element in Noncommutative Geometry
We question the emergence of a minimal length in quantum spacetime, comparing
two notions that appeared at various points in the literature: on the one side,
the quantum length as the spectrum of an operator L in the Doplicher
Fredenhagen Roberts (DFR) quantum spacetime, as well as in the canonical
noncommutative spacetime; on the other side, Connes' spectral distance in
noncommutative geometry. Although on the Euclidean space the two notions merge
into the one of geodesic distance, they yield distinct results in the
noncommutative framework. In particular on the Moyal plane, the quantum length
is bounded above from zero while the spectral distance can take any real
positive value, including infinity. We show how to solve this discrepancy by
doubling the spectral triple. This leads us to introduce a modified quantum
length d'_L, which coincides exactly with the spectral distance d_D on the set
of states of optimal localization. On the set of eigenstates of the quantum
harmonic oscillator - together with their translations - d'_L and d_D coincide
asymptotically, both in the high energy and large translation limits. At small
energy, we interpret the discrepancy between d'_L and d_D as two distinct ways
of integrating the line element on a quantum space. This leads us to propose an
equation for a geodesic on the Moyal plane.Comment: 29 pages, 2 figures. Minor corrections to match the published versio
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