Exact phase space functional for two-body systems

The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently be obtained by minimizing the ground-state energy.Comment: Latex, 12 page

Connes' interpretation of the Standard Model and massive neutrinos

Massive neutrinos can be accommodated into the noncommutative geometry reinterpretation of the Standard Model. The constrained Standard Model Lagrangian is computed anew under the assumption of nonzero neutrino masses. This gives the ``prediction" of a mass for the Higgs particle somewhat higher than in the vanishing neutrino mass case.Comment: Final version, to appear in Phys Lett

A Renormalization Group Analysis of the NCG constraints m_{top} = 2\,m_W}, mHiggs=3.14 mWm_{Higgs} = 3.14 \, m_W

We study the evolution under the renormalization group of the restrictions on the parameters of the standard model coming from Non-Commutative Geometry, namely $m_{top} = 2\,m_W$ and $m_{Higgs} = 3.14 \, m_W$. We adopt the point of view that these relations are to be interpreted as {\it tree level} constraints and, as such, can be implemented in a mass independent renormalization scheme only at a given energy scale $\mu_0$. We show that the physical predictions on the top and Higgs masses depend weakly on $\mu_0$.Comment: 7 pages, FTUAM-94/2, uses harvma

Quasi-pinning and entanglement in the lithium isoelectronic series

The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank-eight approximation we find well-defined families of saturation conditions.Comment: 22 pages, 6 figures, minor changes, references adde

Noncommutative field theory on Rλ3\mathbb{R}^3_\lambda

We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a foliation of $\mathbb{R}^3$ into fuzzy spheres. We first review the construction of a natural matrix basis adapted to $\mathbb{R}^3_\lambda$. We thus consider the problem of defining a new Laplacian operator for the deformed algebra. We propose an operator which is not of Jacobi type. The implication for field theory of the new Laplacian is briefly discussed.Comment: 12 pages. Conference proceedings. Presented at the workshop "Noncommutative Field theory and Gravity" Corfu 201

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

"Everyday Art": Educational Project for today's school

El proyecto educativo «El Arte de cada día» pretende incorporar el mundo de la creación artística así como a sus autores, los artistas, a la actividad diaria de los colegios. Desea acercar a los alumnos los procesos creativos de estos artistas para dar a conocer la importancia que tienen los desarrollos intelectuales en la generación del arte. Consiste en la exposición, cada trimestre escolar, de la obra de un artista en un espacio expositivo habilitado para este fi n en el colegio, quien tiene una charla con los alumnos para compartir sus proceso de trabajo; cómo surgen las ideas y cuál es su desarrollo, otros artistas que le han infl uido, técnicas de ejecución, etc. Posteriormente los alumnos realizarán un trabajo artístico basado en lo aprendido y en conexión con el currículum académico. Estos trabajos serán a su vez expuestos en el espacio expositivo que acogió en un principio a los ar tistas. Todas las exposiciones permanecen abiertas fuera de horario escolar con el fin de que las familias de los alumnos y el público en general puedan también visitarlas.The educational project «Everyday Art» tries to incorporate the world of artistic creation, including the authors and the artists, to the everyday activities at school. It aims at bringing students closer to the creative processes of these artists. Its main purpose is to raise awareness of the importance of the intellectual development in the generation of art. Each school term, the work of an artist is exhibited in an exhibition room arranged in the school. Later, artists share with students how they carry out their work, how ideas arise and develop, how other artists have an infl uence on them and on their work, their preferred art techniques, etc. Afterwards, students prepare an artistic work based on what they have learned, and linked to the academic curriculum. These works will be displayed in the same exhibition room which held the work of the artist. All exhibitions stay open out of school hours so that they can be visited by the students’ families and the general public