Anomalous Commutator Algebra for Conformal Quantum Mechanics

The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived.Comment: 23 pages. A few typos corrected in the final version (which agrees with the published Phys. Rev. D article

Renormalization of the Inverse Square Potential

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energy-dependent s-wave scattering matrix element.Comment: 5 page

Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchange

La imagen Jesuítico-Guaraní: presentatio y equivalencia lingüística

The psychic impact of the banner-painting is registered since the times of evangelization in Guayrá. In the Tupã Róga("Casa de Dios") thereception of the image by the Guaranícontinues to be translated into a magical-shamanic channel: the images are, like words, bearers of spirit: apparitions.Added to the nature of that reception is an interpretive layer that pairs verbal and visual signs. The word, which the pre-Hispanic Guaranílinks to the different manifestations of the soul, under the Jesuit experience maintains its meaning and éschatos, with linguistic equivalences that propitiate deviations or lateralities in the theological sense. The Catecismo de la Lengua Guaraní(1640)revealsto what extent the search for such equivalences leads to different constructions of meaning. Essential words, such as "soul", "image", "Glory" or "hell" echo on different planes, according to the semantic demands of the transmitting sign and the adaptations that the receiving moldcreates. In the case of images, their re-signification is analogous.El impacto psíquico de la pintura-estandarte está documentado desde los tiempos de evangelización en el Guayrá. En la Tupã Róga (“Casa de Dios”) la recepción de la imagen por parte del guaraní continúa traduciéndose en un cauce mágico-chamánico: las imágenes son, como las palabras, portadoras de espíritu: apariciones. Sumada a la naturaleza de esa recepción, hay una capa interpretativa que empareja los signos verbales a los visuales.La palabra, que el guaraní prehispánico vincula a las diferentes manifestaciones del alma, bajo la experiencia jesuítica mantiene su significación y éschatos, con equivalencias lingüísticas que propician desvíos o lateralidades en el sentido teológico. El Catecismo de la Lengua Guaraní(1640) revela hasta qué punto la búsqueda de dichas equivalencias acarrea diferentes construcciones de sentido. Palabras esenciales, tales como “alma”, “imagen”,“Gloria” o “infierno” resuenan en planos diferentes, según las urgencias semánticas del signo emisor y las adaptaciones que la matriz receptora propicia. En el caso de las imágenes, su re-significación es análoga