Global boundary conditions for the Dirac operator

Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional determinants for Dirac operators on manifolds with boundary are considered. The functional determinant for a Dirac operator on a bidimensional disk, in the presence of an Abelian gauge field and subject to global boundary conditions of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship with the index theorem is also commented.Comment: 13 pages, RevTeX. Talk given at the Trends in Theoretical Physics, CERN - Santiago de Compostela - La Plata Meeting, April 27 to May 6, 1997, La Plata, Argentin

Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics

We consider the self-adjoint extensions (SAE) of the symmetric supercharges and Hamiltonian for a model of SUSY Quantum Mechanics in $\mathbb{R}^+$ with a singular superpotential. We show that only for two particular SAE, whose domains are scale invariant, the algebra of N=2 SUSY is realized, one with manifest SUSY and the other with spontaneously broken SUSY. Otherwise, only the N=1 SUSY algebra is obtained, with spontaneously broken SUSY and non degenerate energy spectrum.Comment: LaTeX. 23 pages and 1 figure (minor changes). Version to appear in the Journal of Physics A: Mat. and Ge

Non-Abelian Monopoles as the Origin of Dark Matter

We suggest that dark matter may be partially constituted by a dilute 't Hooft-Polyakov monopoles gas. We reach this conclusion by using the Georgi-Glashow model coupled to a dual kinetic mixing term $F{\tilde {\cal G}}$ where $F$ is the electromagnetic field and ${\cal G}$ the 't Hooft tensor. We show that these monopoles carry both (Maxwell) electric and (Georgi-Glashow) magnetic charges and the electric charge quantization condition is modified in terms of a dimensionless real parameter. This parameter could be determined from milli-charged particle experiments.Comment: 5 pp, no figure

Spectral functions of non essentially selfadjoint operators

One of the many problems to which J.S. Dowker devoted his attention is the effect of a conical singularity in the base manifold on the behavior of the quantum fields. In particular, he studied the small-$t$ asymptotic expansion of the heat-kernel trace on a cone and its effects on physical quantities, as the Casimir energy. In this article we review some peculiar results found in the last decade, regarding the appearance of non-standard powers of $t$, and even negative integer powers of $\log{t}$, in this asymptotic expansion for the selfadjoint extensions of some symmetric operators with singular coefficients. Similarly, we show that the $\zeta$-function associated to these selfadjoint extensions presents an unusual analytic structure.Comment: 57 pages, 1 figure. References added. Version to appear in the special volume of Journal of Physics A in honor of Stuart Dowker's 75th birthday. PACS numbers: 02.30.Tb, 02.30.Sa, 03.65.D

Casimir energy for a scalar field with a frequency dependent boundary condition

We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cut-off is described in terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic expansion for Bessel functions allows to determine the dominant (volume, area, >...) terms in the Casimir energy. The possible interest of this kind of models for dielectric media (and its application to sonoluminescence) is also discussed.Comment: 7 pages, RevTeX. Version to appear in PRD (Introduction enlarged, references added

Towards modelling group-robot interactions using a qualitative spatial representation

This paper tackles the problem of finding a suitable qualitative representation for robots to reason about activity spaces where they carry out tasks interacting with a group of people. The Qualitative Spatial model for Group Robot Interaction (QS-GRI) defines Kendon-formations depending on: (i) the relative location of the robot with respect to other individuals involved in that interaction; (ii) the individuals' orientation; (iii) the shared peri-personal distance; and (iv) the role of the individuals (observer, main character or interactive). The evolution of Kendon-formations between is studied, that is, how one formation is transformed into another. These transformations can depend on the role that the robot have, and on the amount of people involved.Postprint (author's final draft

Qualitative distances and qualitative description of images for indoor scene description and recognition in robotics

This thesis is focused on reducing the gap between the acquisition of low level information by robot sensors and the need of obtaining high level information for enhancing human-machine communication and for applying logical reasoning processes. To this end, approaches for qualitative and semantic image description and qualitative distance sensor interpretation were developed. Experimentation was carried out on di↵erent robotic platforms showing useful applications