Position-dependent noncommutative products: classical construction and field theory

We look in Euclidean $R^4$ for associative star products realizing the commutation relation $[x^\mu,x^\nu]=i\Theta^{\mu\nu}(x)$, where the noncommutativity parameters $\Theta^{\mu\nu}$ depend on the position coordinates $x$. We do this by adopting Rieffel's deformation theory (originally formulated for constant $\Theta$ and which includes the Moyal product as a particular case) and find that, for a topology $R^2 \times R^2$, there is only one class of such products which are associative. It corresponds to a noncommutativity matrix whose canonical form has components $\Theta^{12}=-\Theta^{21}=0$ and $\Theta^{34}=-\Theta^{43}= \theta(x^1,x^2)$, with $\th(x^1,x^2)$ 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 $n\geq 3$ arbitrary dimensions and use it to find traveling noncommutative lumps generalizing noncommutative solitons discussed in the literature. Next we consider Euclidean $\lambda\phi^4$ 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 $\Theta$.Comment: 1+22 pages, no figure

Trouble with space-like noncommutative field theory

It is argued that the one-loop effective action for space like noncommutative (i) lambda phi(4) scalar field theory and (ii) U(1) gauge theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity

Noncommutative spacetime symmetries: Twist versus covariance

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in $(x,\Theta)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.Comment: 19 pages in revtex, references adde

Problemas del Diseño en la Era de la Digitalización. Hand vs. Freehand.

Este artículo constituye una reflexión valorativa y crítica acerca de las consecuencias de la actual hegemonía informática en el ámbito del diseño gráfico, su docencia, práctica y aprendizaje. En él se analiza el contexto sociológico del fenómeno informático, para posteriormente pasar a valorar la situación concreta de su introducción en los procesos creativos del diseño, tanto a un nivel metodológico como práctico. Asimismo, se realiza una consideración acerca de la creciente instrumentalización de los procesos creativos, y de algunas consecuencias negativas al nivel de la formación integral del alumno de artes plásticas y diseño

TECHNICAL AND PHYSIOLOGICAL RESPONSES OF SWIMMING CRAWLSTROKE USING HAND PADDLES, FINS AND SNORKEL IN SWIMMING FLUME: A PILOT STUDY

We evaluated the effect on front-crawl during a 5 minutes effort in a swimming flume, at a speed 95% of 400m wearing swimming paddles, fins or frontal snorkel. It was evaluated measuring changes on stroke frequency, stroke length, ERP, lactate concentration and pulse rate post-effort. An one-way repeated measures ANOVA showed the stroke frequency was significantly affected F(2.3, 27.6) = 20.69