19,045 research outputs found
A Possible Origin of Dark Matter, Dark Energy, and Particle-Antiparticle Asymmetry
In this paper we present a possible origin of dark matter and dark energy
from a solution of the Einstein's equation to a primordial universe, which was
presented in a previous paper. We also analyze the Dirac's equation in this
primordial universe and present the possible origin of the
particle-antiparticle asymmetry. We also present ghost primordial particles as
candidates to some quantum vacuum contituents.Comment: 19 pages,no figure
Mapping Among Manifolds III
In two previous papers, we constructed two modified Hamiltonian formalisms to
make maps among manifolds explicit. In this paper, the two modified formalisms
were adapted to manifolds with local coordinates given by scalar fields, as in
a classical nonlinear sigma-model. The scalar field coordinates could be built
from vectors, tensors, spinors, Lagrangians, Hamiltonians, group parameters,
etc.Comment: 8 pages, no figure
Topics in Non-Riemannian Geometry
In this paper, we present some new results on non-Riemannian geometry, more
specifically, asymmetric connections and Weyl's geometry. For asymmetric
connections, we show that a projective change in the symmetric part generates a
vector field that its not arbitrary, as usually presented, but rather, the
gradient of a non-arbitrary scalar function. We use normal coordinates for the
symmetric part of asymmetric connections as well as for the Weyl's geometry.
This has a direct impact on asymmetric conections, although normal frames are
usual in antisymmetic connections, unlike normal coordinates. In this symmetric
part of asymmetric connections, the vector fields obeys a well-known partial
differential equantion, whereas in Weyl's geometry, gauge vector fields obey an
equation that we believe is presented for the first time in this paper. We
deduce the exact solution of each of these vector fields as the gradient of a
scalar function. For both asymmetric and Weyl's symmetric connections, the
respective scalar functions obey respective scalar partial differential
equations. As a consequence, Weyl's geometry is a conformal differential
geometry and is associated with asymmetric geometry by a projective change. We
also show that a metric tensor naturally appears in asymmetric geometry and is
not introduced via a postulate, as is usually done. In Weyl's geometry, the
eletromagnetic gauge is the gradient of a non-arbitrary scalar function and
eletromagnetic fields are null. Despide the origin in Weyl's differential
geometry, the use of the eletromagnetic gauge is correct in Lagrangean and
Hamiltonian formulations of field theories.Comment: 11 pages, no figures, last versio
The motion of a charged particle in Kalusa-Klein manifolds
In this paper we use Jacobi fields to describe the motion of a charged
particle in the classical gravitational, electromagnetic, and Yang-Mills
fields.Comment: 8 pages, Mikte
Exact Solutions of Einstein Equations
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact
solutions of Einstein equations for a scalar and massive field. The solutions
have a permanent or transitory inflationary behavior.Comment: 06 pages, Latex 2.09, no figure
Physical Principles Based on Geometric Properties
In this paper we present some results obtained in a previous paper about the
Cartan's approach to Riemannian normal coordinates and our conformal
transformations among pseudo-Riemannian manifolds. We also review the classical
and the quantum angular momenta of a particle obtained as a consequence of
geometry, without postulates. We present four classical principles, identifed
as new results obtained from geometry. One of them has properties similar
Heisemberg's uncertaintly principle and another has some properties similar to
Bohr's principle. Our geometric result can be considered as a possible starting
point toward a quantum theory without forces.Comment: 25 pages, no figure
Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations II
In this paper, we have reintroduced a new approach to conformal geometry
developed and presented in two previous papers, in which we show that all
n-dimensional pseudo-Riemannian metrics are conformal to a flat n-dimensional
manifold as well as an n-dimensional manifold of constant curvature when
Riemannian normal coordinates are well-behaved in the origin and in their
neighborhood. This was based on an approach developed by French mathematician
Elie Cartan. As a consequence of geometry, we have reintroduced the classical
and quantum angular momenta of a particle and present new interpretations. We
also show that all n-dimensional pseudo-Riemannian metrics can be embedded in a
hyper-cone of a flat n+2-dimensional manifold.Comment: 33 pages,no figures. Paper of a talk given at the 14th International
Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June
2012
Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations
In this paper we extend the Cartan's approach of Riemannian normal
coordinates and show that all n-dimensional pseudo-Riemannian metrics are
conformal to a flat manifold, when, in normal coordinates, they are
well-behaved in the origin and in its neighborhood. We show that for this
condition all n-dimensioanl pseudo-Riemannian metrics can be embedded in a
hyper-cone of an n+2-dimensional flat manifold. Based on the above conditions
we show that each n-dimensional pseudo-Riemannian manifolds is conformal to an
n-dimensional manifold of constant curvature. As a consequence of geometry,
without postulates, we obtain the classical and the quantum angular momenta of
a particle.Comment: 27 pages, no figure
Mapping and Embedding of Two Metrics Associated with Dark Matter, Dark Energy, and Ordinary Matter
In this paper we build a mapping between two different metrics and embed them
in a flat manifold. One of the metrics represents the ordinary matter, and the
other describes the dark matter, the dark energy, and the particle-antiparticle
asymmetry. The latter was obtained in a recent paper. For the mapping and
embedding, we use two new formalisms developed and presented in two previous
papers, Mapping Among Manifolds and, Conformal Form of Pseudo-Riemannian
Metrics by Normal Coordinate Transformations, which was a generalization of the
Cartan's approach of Riemannian normal coordinates.Comment: 25 pages, no figure
From the 2nd Law of Thermodynamics to AC-Conductivity Measures of Interacting Fermions in Disordered Media
We study the dynamics of interacting lattice fermions with random hopping
amplitudes and random static potentials, in presence of time-dependent
electromagnetic fields. The interparticle interaction is short-range and
translation invariant. Electromagnetic fields are compactly supported in time
and space. In the limit of infinite space supports (macroscopic limit) of
electromagnetic fields, we derive Ohm and Joule's laws in the AC-regime. An
important outcome is the extension to interacting fermions of the notion of
macroscopic AC-conductivity measures, known so far only for free fermions with
disorder. Such excitation measures result from the 2nd law of thermodynamics
and turn out to be L\'{e}vy measures. As compared to the Drude
(Lorentz--Sommerfeld) model, widely used in Physics, the quantum many-body
problem studied here predicts a much smaller AC-conductivity at large
frequencies. This indicates (in accordance with experimental results) that the
relaxation time of the Drude model, seen as an effective parameter for the
conductivity, should be highly frequency-dependent. We conclude by proposing an
alternative effective description - using L\'{e}vy Processes in Fourier space -
of the phenomenon of electrical conductivity
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