7,598 research outputs found
On Clifford Subalgebras, Spacetime Splittings and Applications
Z2-gradings of Clifford algebras are reviewed and we shall be concerned with
an alpha-grading based on the structure of inner automorphisms, which is
closely related to the spacetime splitting, if we consider the standard
conjugation map automorphism by an arbitrary, but fixed, splitting vector.
After briefly sketching the orthogonal and parallel components of products of
differential forms, where we introduce the parallel [orthogonal] part as the
space [time] component, we provide a detailed exposition of the Dirac operator
splitting and we show how the differential operator parallel and orthogonal
components are related to the Lie derivative along the splitting vector and the
angular momentum splitting bivector. We also introduce multivectorial-induced
alpha-gradings and present the Dirac equation in terms of the spacetime
splitting, where the Dirac spinor field is shown to be a direct sum of two
quaternions. We point out some possible physical applications of the formalism
developed.Comment: 22 pages, accepted for publication in International Journal of
Geometric Methods in Modern Physics 3 (8) (2006
Study of models of the sine-Gordon type in flat and curved spacetime
We study a new family of models of the sine-Gordon type, starting from the
sine-Gordon model, including the double sine-Gordon, the triple one, and so on.
The models appears as deformations of the starting model, with the deformation
controlled by two parameters, one very small, used to control a linear
expansion on it, and the other, which specifies the particular model in the
family of models. We investigate the presence of topological defects, showing
how the solutions can be constructed explicitly from the topological defects of
the sine-Gordon model itself. In particular, we delve into the double
sine-Gordon model in a braneworld scenario with a single extra dimension of
infinite extent, showing that a stable gravity scenario is admissible. Also, we
briefly show that the deformation procedure can be used iteratively, leading to
a diversity of possibilities to construct families of models of the sine-Gordon
type.Comment: 8 pages, 7 figures; Title changed, author and new results included;
version to appear in EPJ
The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential
Recently Kiriushcheva and Kuzmin claimed to have shown that the
Einstein-Hilbert Lagrangian cannot be written in any coordinate gauge as an
exact differential in a 2-dimensional spacetime. Since this is contrary to
other statements on the subject found in the literature, as e.g., by Deser and
Jackiw, Jackiw, Grumiller, Kummer and Vassilevich it is necessary to do decide
who has reason. This is done in this paper in a very simply way using the
Clifford bundle formalism. In this version we added Section 18 which discusses
a recent comment on our paper just posted by Kiriushcheva and Kuzmin.Comment: 11 pages, Misprints in some equations have been corrected; four new
references have been added, Section 18 adde
Statistical Mechanics Characterization of Neuronal Mosaics
The spatial distribution of neuronal cells is an important requirement for
achieving proper neuronal function in several parts of the nervous system of
most animals. For instance, specific distribution of photoreceptors and related
neuronal cells, particularly the ganglion cells, in mammal's retina is required
in order to properly sample the projected scene. This work presents how two
concepts from the areas of statistical mechanics and complex systems, namely
the \emph{lacunarity} and the \emph{multiscale entropy} (i.e. the entropy
calculated over progressively diffused representations of the cell mosaic),
have allowed effective characterization of the spatial distribution of retinal
cells.Comment: 3 pages, 1 figure, The following article has been submitted to
Applied Physics Letters. If it is published, it will be found online at
http://apl.aip.org
Bounds on topological Abelian string-vortex and string-cigar from information-entropic measure
In this work we obtain bounds on the topological Abelian string-vortex and on
the string-cigar, by using a new measure of configurational complexity, known
as configurational entropy. In this way, the information-theoretical measure of
six-dimensional braneworlds scenarios are capable to probe situations where the
parameters responsible for the brane thickness are arbitrary. The so-called
configurational entropy (CE) selects the best value of the parameter in the
model. This is accomplished by minimizing the CE, namely, by selecting the most
appropriate parameters in the model that correspond to the most organized
system, based upon the Shannon information theory. This information-theoretical
measure of complexity provides a complementary perspective to situations where
strictly energy-based arguments are inconclusive. We show that the higher the
energy the higher the CE, what shows an important correlation between the
energy of the a localized field configuration and its associated entropic
measure.Comment: 6 pages, 7 figures, final version to appear in Phys. Lett.
New constrained generalized Killing spinor field classes in warped flux compactifications
The generalized Fierz identities are addressed in the K\"ahler-Atiyah bundle
framework from the perspective of the equations governing constrained
generalized Killing spinor fields. We explore the spin geometry in a Riemannian
8-manifold composing a warped flux compactification AdS, whose
metric and fluxes preserve one supersymmetry in AdS. Supersymmetry
conditions can be efficiently translated into spinor bilinear covariants, whose
algebraic and differential constraints yield identifying new spinor field
classes. Intriguing implications and potential applications are discussed.Comment: 25 page
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