179 research outputs found
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 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 where is the electromagnetic field and 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- 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 , and even
negative integer powers of , in this asymptotic expansion for the
selfadjoint extensions of some symmetric operators with singular coefficients.
Similarly, we show that the -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} -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
A calculation with a bi-orthogonal wavelet transformation
We explore the use of bi-orthogonal basis for continuous wavelet
transformations, thus relaxing the so-called admissibility condition on the
analyzing wavelet. As an application, we determine the eigenvalues and
corresponding radial eigenfunctions of the Hamiltonian of relativistic
Hydrogen-like atoms.Comment: 18 pages, see instead physics/970300
Dirac Operator on a disk with global boundary conditions
We compute the functional determinant for a Dirac operator in the presence of
an Abelian gauge field on a bidimensional disk, under global boundary
conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the
connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde
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