Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory

The underlying reasons for the difficulty of unitarily implementing the whole conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are investigated in this paper. Firstly, we demonstrate that the singular action of the subgroup of special conformal transformations (SCT), on the standard Minkowski space $M$, cannot be primarily associated with the vacuum radiation problems, the reason being more profound and related to the dynamical breakdown of part of the conformal symmetry (the SCT subgroup, to be more precise) when representations of null mass are selected inside the representations of the whole conformal group. Then we show how the vacuum of the massless QFT radiates under the action of SCT (usually interpreted as transitions to a uniformly accelerated frame) and we calculate exactly the spectrum of the outgoing particles, which proves to be a generalization of the Planckian one, this recovered as a given limit.Comment: 29 pages, Latex, 1 figure, to appear in Commun. Math. Phy

Two dimensional dynamical systems which admit Lie and Noether symmetries

We prove two theorems which relate the Lie point symmetries and the Noether symmetries of a dynamical system moving in a Riemannian space with the special projective group and the homothetic group of the space respectively. The theorems are applied to classify the two dimensional Newtonian dynamical systems, which admit a Lie point/Noether symmetry. Two cases are considered, the non-conservative and the conservative forces. The use of the results is demonstrated for the Kepler - Ermakov system, which in general is non-conservative and for potentials similar to the H\`enon Heiles potential. Finally it is shown that in a FRW background with no matter present, the only scalar cosmological model which is integrable is the one for which 3-space is flat and the potential function of the scalar field is exponential. It is important to note that in all applications the generators of the symmetry vectors are found by reading the appropriate entry in the relevant tables.Comment: 25 pages, 17 table

Spinal NKCC1 blockade inhibits TRPV1-dependent referred allodynia

Background The Na+, K+, 2Cl- type I cotransporter (NKCC1) and TRPV1 receptors, at the level of the dorsal horn, have been implicated in mediating allodynia in response to an inflammatory insult. The NKCC1 cotransporter regulates intracellular [Cl-] and thus the magnitude and polarity of GABAA receptor responses in neurons. TRPV1 receptors transduce diverse chemical and natural stimuli in nociceptors and are critical for inflammatory hyperalgesia.Results Here we have tested the role of spinal NKCC1 cotransporters and TRPV1 receptors in referred allodynia in a model of visceral hyperalgesia in mice. Intrathecal (IT) injection of the NKCC1 inhibitor bumetanide (BUM, 1 nmol) inhibited referred, abdominal allodynia evoked by an intracolonic capsaicin injection. BUM was effective when injected IT either before or up to 4 hrs after the establishment of referred allodynia. The TRPV1 antagonist AMG 9810 (1 nmol) also inhibited referred allodynia in this model suggesting the involvement of an endogenous TRPV1 agonist in the dorsal horn in referred allodynia. In support of this suggestion, the endovanilloid TRPV1 agonist, narachidonoyl- dopamine (NADA, 1 or 10 nmol, IT) evoked stroking allodynia in the hindpaw that was blocked by co-treatment with AMG 9810 (1 nmol). The TRPV1-dependent stroking allodynia caused by NADA appeared to be functionally linked to NKCC1 because BUM (1 nmol) also inhibited NADA-evoked stroking allodynia.Conclusion Our findings indicate that spinal NKCC1 and TRPV1 are critical for referred allodynia mediated by a painful visceral stimulus. Moreover, they suggest that endogenous TRPV1 agonists, released in the CNS in painful conditions, might stimulate TRPV1 receptors on primary afferents that, in turn, play a role in increasing NKCC1 activity leading to allodynia.This work was supported by the National Institutes for Neurological Disorders and Stroke (NINDS, DA19959, to TJP), the American Pain Society (to TJP), the Spanish Secretaria de Estado de Educacion y Universidades: Formacion de Profesorado Universitario Grant (to JME), the Canadian Foundation for Innovation (CFI, to FC), the Canadian Institutes of Health Research (CIHR, to FC) and the Fonds de la recherche en santé du Québec (FRSQ, to FC)

Influencia de la vía de abordaje y de posición de la cúpula acetabular en la luxación de la artroplastia total de cadera: estudio caso-control

Tanto la vía de acceso quirúrgica como la posición de los componentes se han relacionado con la presencia de una luxación en las artroplastias primarias de cadera. Hemos estudiado la presencia de esta complicación en una serie de 758 artroplastias no cementadas modelo Bihapro. Encontramos 21 luxaciones. Por otro lado se seleccionó de forma aleatoria un grupo de control de 42 pacientes que no habían presentado luxación. Se diseñó un estudio de casos y controles que englobaba por tanto a 63 pacientes que tenían implantada una artroplastia de este modelo. En el grupo de casos observamos que el porcentaje de luxación fue sensiblemente mayor en el sexo masculino con un 66,7%, en comparación con el sexo femenino que fue de un 42,8% aunque esta diferencia no fue estadísticamente significativa. No se observaron diferencias en la frecuencia de luxaciones en relación con la vía anterior o lateral, pero sin embargo en la vía posterior la luxación se produjo en un solo caso (4,8% de todas las luxaciones) con una incidencia claramente menor que en los abordajes anterior y lateral, siendo esta diferencia estadísticamente significativa (p=0,005). También observamos diferencias estadísticamente significativas en cuanto a un mayor porcentaje de luxaciones cuando la inclinación del componente acetabular era mayor de 50º (76,2%), o cuando la anteversión del cotilo era mayor o igual a 20º (54,4%). La vía de abordaje posterior con reconstrucción capsular y muscular presenta un menor porcentaje de luxación después de una artroplastia primaria en comparación con la anterior o lateral. Una inclinación mayor de 50º o una anteversión mayor de 20º favorecen la presencia de una luxación.The surgical approach and the cup position have been related with the dislocations of total hip arthroplasty. We have studied the presence of this complication in 758 Bihapro™ cementless arthroplasties. We got a case group of 21 dislocations; then we selected a control group of 42 patients without luxation to design a case-control study. The case group had a higher rate of dislocation in males (66.7 % versus 42.8 % in females) although this difference was not statistically significant. We didn’t observe any difference in the frequency of luxations relating to the anterior or lateral surgical approach, however in the posterior approach the dislocation appeared only in one case (4.8 % of the all dislocations) with statistically differences (p=0.005). We also observed statistically significant differences of luxations when the acetabular cup inclination was higher than 50º (76.2 %), or when the cup anteversion was equal or higher than 20º (52.4 %). The posterior surgical approach with capsular and muscular suture presented a lower rate of dislocation after a primary arthroplasty compared with the anterior or lateral approachs. An inclination bigger than 50º or an anteversion bigger than 20º seems to be a risk factor of luxation

Cosmological Analogues of the Bartnik--McKinnon Solutions

We present a numerical classification of the spherically symmetric, static solutions to the Einstein--Yang--Mills equations with cosmological constant $\Lambda$. We find three qualitatively different classes of configurations, where the solutions in each class are characterized by the value of $\Lambda$ and the number of nodes, $n$, of the Yang--Mills amplitude. For sufficiently small, positive values of the cosmological constant, \Lambda < \Llow(n), the solutions generalize the Bartnik--McKinnon solitons, which are now surrounded by a cosmological horizon and approach the deSitter geometry in the asymptotic region. For a discrete set of values $\Lambda_{\rm reg}(n) > \Lambda_{\rm crit}(n)$, the solutions are topologically $3$--spheres, the ground state $(n=1)$ being the Einstein Universe. In the intermediate region, that is for \Llow(n) < \Lambda < \Lhig(n), there exists a discrete family of global solutions with horizon and ``finite size''.Comment: 16 pages, LaTeX, 9 Postscript figures, uses epsf.st