Quantum Inverse Square Interaction

Hamiltonians with inverse square interaction potential occur in the study of a variety of physical systems and exhibit a rich mathematical structure. In this talk we briefly mention some of the applications of such Hamiltonians and then analyze the case of the N-body rational Calogero model as an example. This model has recently been shown to admit novel solutions, whose properties are discussed.Comment: Talk presented at the conference "Space-time and Fundamental Interactions: Quantum Aspects" in honour of Prof. A.P.Balachandran's 65th birthday, Vietri sul Mare, Italy, 26 - 31 May, 2003, Latex file, 9 pages. Some references added in the replaced versio

Spacetime Emergence in the Robertson-Walker Universe from a Matrix model

Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system describes either a relativistic particle in the Robertson-Walker background, or metric fluctuations of the Robertson-Walker geometry. Moreover we derive a tree-level M-theory matrix model in this time-dependent background. Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzy near the big bang, while the classical Robertson-Walker geometry emerges as the Universe expands. From our approach we also derive the temperature of the Universe interpolating between the radiation and matter dominated eras.Comment: 4 pages - accepted for publication in Physical Review Letter

A note about the t`Hooft`s ansatz for SU(N) real time guage theories

The t`Hooft's ansatz reduces the classical Yang--Mills theory to the $\lambda\phi^4$ one. It is shown that in the frame of this ansatz the real-time classical solutions for the arbitrary SU(N) gauge group is obtained by embedding $SU(2)\times SU(2)$ into SU(N). It is argued that this group structure is the only possibility in the frame of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown

Horizons and the Thermal Harmonic Oscillator

We show that two-dimensional anti-de Sitter spacetime (AdS_2) can be put in correspondence, holographically, both with the harmonic oscillator and the free particle. When AdS_2 has an horizon the corresponding mechanical system is a thermal harmonic oscillator at temperature given by the Hawking temperature of the horizon.Comment: Content changed, title slightly modifie

Fermion propagators in space-time

The one- and the two-particle propagators for an infinite non-interacting Fermi system are studied as functions of space-time coordinates. Their behaviour at the origin and in the asymptotic region is discussed, as is their scaling in the Fermi momentum. Both propagators are shown to have a divergence at equal times. The impact of the interaction among the fermions on their momentum distribution, on their pair correlation function and, hence, on the Coulomb sum rule is explored using a phenomenological model. Finally the problem of how the confinement is reflected in the momentum distribution of the system's constituents is briefly addressed.Comment: 26 pages, 9 figures, accepted for publication on Phys. Rev.

Nucleon and delta masses in QCD

Using the positivity of the path integral measure of $QCD$ and defining a structure for the quark propagator in a background field according to the fluxon scenario for confinement, we calculate and compare the correlators for nucleon and delta. From their shape we elucidate about the origin of their mass difference, which in our simplified scenario is due to the tensor structure in the propagator. This term arises due to a dynamical mechanism which is responsible simultaneously for confinement and spontaneous chiral symmetry breaking. Finally we discuss, by comparing the calculated correlators with the Lehmann representation, the possibility that a strong CP and/or P violation occurs as a consequence of a specific mechanism for confinement.Comment: Latex, FTUV/92-2

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure

About the Poisson Structure for D4 Spinning String

The model of D4 open string with non-Grassmann spinning variables is considered. The non-linear gauge, which is invariant both Poincar\'e and scale transformations of the space-time, is used for subsequent studies. It is shown that the reduction of the canonical Poisson structure from the original phase space to the surface of constraints and gauge conditions gives the degenerated Poisson brackets. Moreover it is shown that such reduction is non-unique. The conseption of the adjunct phase space is introduced. The consequences for subsequent quantization are discussed. Deduced dependence of spin $J$ from the square of mass $\mu^2$ of the string generalizes the ''Regge spectrum`` for conventional theory.Comment: 23 page

Non-commutativity as a measure of inequivalent quantization

We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model we consider the inverse square problem in non-commutative space. The scale invariance of the system is known to be explicitly broken by the scale of non-commutativity \Theta. The resulting problem in non-commutative space is analyzed. It is shown that despite the presence of higher singular potential coming from the leading term of the expansion of the potential to first order in \Theta, it can have a self-adjoint extensions. The boundary conditions are obtained, belong to a 1-parameter family and related to the strength of non-commutativity.Comment: 4 pages, 2 figures, revte

Caracteres preimaginales y aspectos bionómicos de Gyriosomus luczotii Laporte, 1840 (Coleoptera, Tenebrionidae)

Se describe la morfología y microestructura coriónica del huevo y la morfología del primer estadio larvario de Gyriosomus luczotii Laporte, 1840 (Coleoptera, Tenebrionidae, Nycteliini). También se exponen antecedentes bionómicos y distribucionales de la especie. Para la obtención de huevos y larvas, se recolectaron parejas en el terreno que fueron mantenidas en cajas de cria hasta la ovoposición y posterior eclosión. La estructura y ornamentación del exocorion del huevo y características morfológicas externas de la larva fueron analizadas mediante microscopía electrónica de barrido. Los resultados muestran que los huevos de G. luczotii presentan un micropilo redondeado y exocorion liso, con células hexagonales sin aeropilos. Las larvas de G. luczotii presentan características morfológicas adaptativas para la vida edáfica del tipo Pedobionta: cápsula cefálica con gran cantidad de sensillas, patas protorácicas de función cavadora, y pigopodio bien desarrollado. Se analiza la importancia de algunos caracteres morfológicos de la larva de primer estadio como criterio de diagnóstico específico y se establece que las diferencias interespecíficas referidas a las sensillas frontales, la forma del clípeo y el margen anterior del labro tienen valor taxonómico y probablemente filogenético. Palabras clave: Tenebrionidae, Gyriosomus, Morfología, Estadios preimaginales, Desierto costero, Chile.Preimaginal characters and bionomical aspects of Gyriosomus luczotii Laporte, 1840 (Coleoptera, Tenebrionidae) We describe the morphology and microstructure of the egg chorion, and the morphology of the first instar larva of Gyriosomus luczotii Laporte, 1840 (Coleoptera, Tenebrionidae, Nycteliini). Bionomical and distributional data on this species are also provided. To obtain eggs and larvae, couples were collected in the field and kept in rearing cages until oviposture and ecclosion. The structure and adornment of the egg exochorion, and the exterior morphological features of larvae were examined with electron scanning microscopy. The eggs of G. luczotii showed a rounded micropyle and a smooth exochorion, composed of hexagonal cells without aeropyles. The larvae of G. luczotii showed morphological characteristics suited for an edaphic life similar to that of Pedobionta: digging prothoracic legs, cephalic capsule with abundant sensilla, and well–developed pygopodium. We analysed the importance of larval morphology as an element for specific diagnosis and found that interspecific differences regarding frontal sensilla, clypeus shape, and anterior part of labrum, had a taxonomic value and possibly a phylogenetic value. Key words: Tenebrionidae, Gyriosomus, Morphology, Preimaginal stages, Coastal desert, Chile.Se describe la morfología y microestructura coriónica del huevo y la morfología del primer estadio larvario de Gyriosomus luczotii Laporte, 1840 (Coleoptera, Tenebrionidae, Nycteliini). También se exponen antecedentes bionómicos y distribucionales de la especie. Para la obtención de huevos y larvas, se recolectaron parejas en el terreno que fueron mantenidas en cajas de cria hasta la ovoposición y posterior eclosión. La estructura y ornamentación del exocorion del huevo y características morfológicas externas de la larva fueron analizadas mediante microscopía electrónica de barrido. Los resultados muestran que los huevos de G. luczotii presentan un micropilo redondeado y exocorion liso, con células hexagonales sin aeropilos. Las larvas de G. luczotii presentan características morfológicas adaptativas para la vida edáfica del tipo Pedobionta: cápsula cefálica con gran cantidad de sensillas, patas protorácicas de función cavadora, y pigopodio bien desarrollado. Se analiza la importancia de algunos caracteres morfológicos de la larva de primer estadio como criterio de diagnóstico específico y se establece que las diferencias interespecíficas referidas a las sensillas frontales, la forma del clípeo y el margen anterior del labro tienen valor taxonómico y probablemente filogenético. Palabras clave: Tenebrionidae, Gyriosomus, Morfología, Estadios preimaginales, Desierto costero, Chile