42 research outputs found
Improved Epstein-Glaser renormalization in x-space versus differential renormalization
Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details
Position-dependent noncommutative products: classical construction and field theory
We look in Euclidean for associative star products realizing the
commutation relation , where the
noncommutativity parameters depend on the position
coordinates . We do this by adopting Rieffel's deformation theory
(originally formulated for constant and which includes the Moyal
product as a particular case) and find that, for a topology ,
there is only one class of such products which are associative. It corresponds
to a noncommutativity matrix whose canonical form has components
and ,
with an arbitrary positive smooth bounded function. In Minkowski
space-time, this describes a position-dependent space-like or magnetic
noncommutativity. We show how to generalize our construction to
arbitrary dimensions and use it to find traveling noncommutative lumps
generalizing noncommutative solitons discussed in the literature. Next we
consider Euclidean field theory on such a noncommutative
background. Using a zeta-like regulator, the covariant perturbation method and
working in configuration space, we explicitly compute the UV singularities. We
find that, while the two-point UV divergences are non-local, the four-point UV
divergences are local, in accordance with recent results for constant .Comment: 1+22 pages, no figure
Surco en cabeza femoral como signo de inestabilidad de cadera en pacientes con Síndrome de Down.
La inestabilidad de cadera en pacientes afectos de síndrome de Down es una entidad poco frecuente,
en la actualidad todavía existe controversia sobre las anomalías anatómicas asociadas. El objetivo de este trabajo es
describir los cambios anatómicos en las caderas de pacientes con inestabilidad en el síndrome de Down (SD). Hemos
revisado las tomografías computarizadas (TC) de los pacientes afectos de luxación de cadera con SD. A tres de los 7
pacientes intervenidos en nuestro centro, se les había realizado TC de caderas. En todas las TC mostraban la presen
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cia de lesión lineal vertical (surco) localizada en región epifisaria, atravesando la fisis, de localización antero-interna.
Creemos que la posición adoptada cuando duermen (flexión, aducto y rotación interna) puede producir hiperpresión
de la cabeza femoral sobre la ceja acetabular posterior, produciendo un surco vertical. La presencia de esta lesión
puede ser sugestiva de inestabilidad subclínica de cadera en ausencia de episodio de luxación.Hip instability in patients with Down syndrome is a rare entity, currently there is still controversy
about the associated anatomical anomalies. The aim of the study is to describe the anatomical changes in the hips of
patients with instability in Down syndrome (DS). We have reviewed the computed tomography (CT) of patients with
hip dislocation with SD. Three of the 7 patients treated in our center are performed CT had hips. All CT showed the
presence of vertical linear lesion (groove) located in epiphyseal region, crossing the physis, antero-internal location.
We believe that the position taken when sleeping (flexion, adduction and internal rotation) can produce overpressure
of the femoral head over the posterior acetabular rim, producing a vertical groove. The presence of this lesion can be
suggestive of subclinical instability in the absence of hip dislocation
Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering
The quantized free Dirac field is considered on Minkowski spacetime (of
general dimension). The Dirac field is coupled to an external scalar potential
whose support is finite in time and which acts by a Moyal-deformed
multiplication with respect to the spatial variables. The Moyal-deformed
multiplication corresponds to the product of the algebra of a Moyal plane
described in the setting of spectral geometry. It will be explained how this
leads to an interpretation of the Dirac field as a quantum field theory on
Moyal-deformed Minkowski spacetime (with commutative time) in a setting of
Lorentzian spectral geometries of which some basic aspects will be sketched.
The scattering transformation will be shown to be unitarily implementable in
the canonical vacuum representation of the Dirac field. Furthermore, it will be
indicated how the functional derivatives of the ensuing unitary scattering
operators with respect to the strength of the non-commutative potential induce,
in the spirit of Bogoliubov's formula, quantum field operators (corresponding
to observables) depending on the elements of the non-commutative algebra of
Moyal-Minkowski spacetime.Comment: 60 pages, 1 figur
A nonperturbative form of the spectral action principle in noncommutative geometry
Using the formalism of superconnections, we show the existence of a bosonic
action functional for the standard K-cycle in noncommutative geometry, giving
rise, through the spectral action principle, only to the Einstein gravity and
Standard Model Yang-Mills-Higgs terms. It provides an effective nonminimal
coupling in the bosonic sector of the Lagrangian.Comment: 12 pages. LaTeX2e, instructions for obsolete LaTeX'
Local Index Formula on the Equatorial Podles Sphere
We discuss spectral properties of the equatorial Podles sphere. As a
preparation we also study the `degenerate' (i.e. ) case (related to the
quantum disk). We consider two different spectral triples: one related to the
Fock representation of the Toeplitz algebra and the isopectral one. After the
identification of the smooth pre--algebra we compute the dimension
spectrum and residues. We check the nontriviality of the (noncommutative) Chern
character of the associated Fredholm modules by computing the pairing with the
fundamental projector of the -algebra (the nontrivial generator of the
-group) as well as the pairing with the -analogue of the Bott
projector. Finally, we show that the local index formula is trivially
satisfied.Comment: 18 pages, no figures; minor correction
Cosmological perturbations and short distance physics from Noncommutative Geometry
We investigate the possible effects on the evolution of perturbations in the
inflationary epoch due to short distance physics. We introduce a suitable non
local action for the inflaton field, suggested by Noncommutative Geometry, and
obtained by adopting a generalized star product on a Friedmann-Robertson-Walker
background. In particular, we study how the presence of a length scale where
spacetime becomes noncommutative affects the gaussianity and isotropy
properties of fluctuations, and the corresponding effects on the Cosmic
Microwave Background spectrum.Comment: Published version, 16 page
Heat kernel and number theory on NC-torus
The heat trace asymptotics on the noncommutative torus, where generalized
Laplacians are made out of left and right regular representations, is fully
determined. It turns out that this question is very sensitive to the
number-theoretical aspect of the deformation parameters. The central condition
we use is of a Diophantine type. More generally, the importance of number
theory is made explicit on a few examples. We apply the results to the spectral
action computation and revisit the UV/IR mixing phenomenon for a scalar theory.
Although we find non-local counterterms in the NC theory on \T^4, we
show that this theory can be made renormalizable at least at one loop, and may
be even beyond
The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
Equivariance under the action of Uq(so(5)) is used to compute the left
regular and (chiral) spinorial representations of the algebra of the orthogonal
quantum 4-sphere S^4_q. These representations are the constituents of a
spectral triple on this sphere with a Dirac operator which is isospectral to
the canonical one on the round undeformed four-sphere and which gives metric
dimension four for the noncommutative geometry. Non-triviality of the geometry
is proved by pairing the associated Fredholm module with an `instanton'
projection. We also introduce a real structure which satisfies all required
properties modulo smoothing operators.Comment: 40 pages, no figures, Latex. v2: Title changed. Sect. 9 on real
structure completely rewritten and results strengthened. Additional minor
changes throughout the pape
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