42,461 research outputs found
Geometric and Extensor Algebras and the Differential Geometry of Arbitrary Manifolds
We give in this paper which is the third in a series of four a theory of
covariant derivatives of representatives of multivector and extensor fields on
an arbitrary open set U of M, based on the geometric and extensor calculus on
an arbitrary smooth manifold M. This is done by introducing the notion of a
connection extensor field gamma defining a parallelism structure on U, which
represents in a well defined way the action on U of the restriction there of
some given connection del defined on M. Also we give a novel and intrinsic
presentation (i.e., one that does not depend on a chosen orthonormal moving
frame) of the torsion and curvature fields of Cartan's theory. Two kinds of
Cartan's connection operator fields are identified, and both appear in the
intrinsic Cartan's structure equations satisfied by the Cartan's torsion and
curvature extensor fields. We introduce moreover a metrical extensor g in U
corresponding to the restriction there of given metric tensor \slg defined on M
and also introduce the concept a geometric structure (U,gamma,g) for U and
study metric compatibility of covariant derivatives induced by the connection
extensor gamma. This permits the presentation of the concept of gauge
(deformed) derivatives which satisfy noticeable properties useful in
differential geometry and geometrical theories of the gravitational field.
Several derivatives operators in metric and geometrical structures, like
ordinary and covariant Hodge coderivatives and some duality identities are
exhibit.Comment: This paper is an improved version of material contained in
math.DG/0501560, math.DG/0501561, math.DG/050200
The central parsecs of active galactic nuclei: challenges to the torus
Type 2 AGN are by definition nuclei in which the broad-line region and
continuum light are hidden at optical/UV wavelengths by dust. Via accurate
registration of infrared (IR) Very Large Telescope adaptive optics images with
optical \textit{Hubble Space Telescope} images we unambiguously identify the
precise location of the nucleus of a sample of nearby, type 2 AGN. Dust
extinction maps of the central few kpc of these galaxies are constructed from
optical-IR colour images, which allow tracing the dust morphology at scales of
few pc. In almost all cases, the IR nucleus is shifted by several tens of pc
from the optical peak and its location is behind a dust filament, prompting to
this being a major, if not the only, cause of the nucleus obscuration. These
nuclear dust lanes have extinctions mag, sufficient to at least
hide the low-luminosity AGN class, and in some cases are observed to connect
with kpc-scale dust structures, suggesting that these are the nuclear fueling
channels. A precise location of the ionised gas H and
[\textsc{Si\,vii}] 2.48 m coronal emission lines relative to those of the
IR nucleus and dust is determined. The H peak emission is often shifted
from the nucleus location and its sometimes conical morphology appears not to
be caused by a nuclear --torus-- collimation but to be strictly defined by the
morphology of the nuclear dust lanes. Conversely, [\textsc{Si\,vii}] 2.48
m emission, less subjected to dust extinction, reflects the truly, rather
isotropic, distribution of the ionised gas. All together, the precise location
of the dust, ionised gas and nucleus is found compelling enough to cast doubts
on the universality of the pc-scale torus and supports its vanishing in
low-luminosity AGN. Finally, we provide the most accurate position of the NGC
1068 nucleus, located at the South vertex of cloud B.Comment: 23 pages, 10 figures, accepted for publication in MNRA
Geometric Algebras and Extensors
This is the first paper in a series (of four) designed to show how to use
geometric algebras of multivectors and extensors to a novel presentation of
some topics of differential geometry which are important for a deeper
understanding of geometrical theories of the gravitational field. In this first
paper we introduce the key algebraic tools for the development of our program,
namely the euclidean geometrical algebra of multivectors Cl(V,G_{E}) and the
theory of its deformations leading to metric geometric algebras Cl(V,G) and
some special types of extensors. Those tools permit obtaining, the remarkable
golden formula relating calculations in Cl(V,G) with easier ones in Cl(V,G_{E})
(e.g., a noticeable relation between the Hodge star operators associated to G
and G_{E}). Several useful examples are worked in details fo the purpose of
transmitting the "tricks of the trade".Comment: This paper (to appear in Int. J. Geom. Meth. Mod. Phys. 4 (6) 2007)
is an improved version of material appearing in math.DG/0501556,
math.DG/0501557, math.DG/050155
Valence fluctuations in a lattice of magnetic molecules: application to iron(II) phtalocyanine molecules on Au(111)
We study theoretically a square lattice of the organometallic Kondo adsorbate
iron(II) phtalocyanine (FePc) deposited on top of Au(111), motivated by recent
scanning tunneling microscopy experiments. We describe the system by means of
an effective Hubbard-Anderson model, where each molecule has degenerate
effective orbitals with and symmetry, which we solve for
arbitrary occupation and arbitrary on-site repulsion . To that end, we
introduce a generalized slave-boson mean-field approximation (SBMFA) which
correctly describes both the non-interacting limit (NIL) and the
strongly-interacting limit , where our formalism
reproduces the correct value of the Kondo temperature for an isolated FePc
molecule. Our results indicate that while the isolated molecule can be
described by an SU(4) Anderson model in the Kondo regime, the case of the
square lattice corresponds to the intermediate-valence regime, with a total
occupation of nearly 1.65 holes in the FePc molecular orbitals. Our results
have important implications for the physical interpretation of the experiment.Comment: 7 pages, 2 figure
A family of complex potentials with real spectrum
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that
is invariant under the combined effects of parity and time reversal
transformation. Numerical investigation shows that for some values of the
potential parameters the hamiltonian operator supports real eigenvalues and
localized eigenfunctions. In contrast with other PT symmetric models, which
require special integration paths in the complex plane, our model is integrable
along a line parallel to the real axis.Comment: Six figures and four table
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