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Quantum States Allowing Minimum Uncertainty Product of angular position and momentum
We provide necessary and sufficient conditions for states to have an
arbitrarily small uncertainty product of the azimuthal angle and its
canonical moment . We illustrate our results with analytical examples
CCDM model from quantum particle creation: constraints on dark matter mass
In this work the results from the quantum process of matter creation have
been used in order to constrain the mass of the dark matter particles in an
accelerated Cold Dark Matter model (Creation Cold Dark Matter, CCDM). In order
to take into account a back reaction effect due to the particle creation
phenomenon, it has been assumed a small deviation for the scale
factor in the matter dominated era of the form .
Based on recent data, the best fit values for the mass of dark matter
created particles and the parameter have been found as
GeV, restricted to a 68.3\% c.l. interval of
() GeV and at
68.3\% c.l. For these best fit values the model correctly recovers a transition
from decelerated to accelerated expansion and admits a positive creation rate
near the present era. Contrary to recent works in CCDM models where the
creation rate was phenomenologically derived, here we have used a quantum
mechanical result for the creation rate of real massive scalar particles, given
a self consistent justification for the physical process. This method also
indicates a possible solution to the so called "dark degeneracy", where one can
not distinguish if it is the quantum vacuum contribution or quantum particle
creation which accelerates the Universe expansion.Comment: 16 pages, 5 figures. Major modifications have been done, following
the referee suggestions. The deduction of the treatment is now more
transparent, figures have been added showing the statistical limits over the
dark matter mass, and the best fit for DM mass has been slightly modifie
Spacetime: Arena or Reality?
For small values of the mass (in relation to the angular momentum and
electric charge), the Kerr-Newman (KN) solution of Einstein equation reduces to
a naked singularity of circular shape. By considering the Hawking and Ellis
extended interpretation of the KN spacetime, as well as Wheeler's idea of
"charge without charge", the non-trivial topological structure of the extended
KN spatial section is found to represent gravitational states with
half-integral angular momentum. As a consequence, it can be consistently
interpreted as a model for the electron-positron system, in which the concepts
of mass, charge and spin emerge from the spacetime geometry. According to this
model, therefore, instead of a simple arena, spacetime must have a concrete
existence, being responsible -- through its highly non-trivial topological
structures -- for the building blocks of (at least some of) the existing matter
in the universe.Comment: Chapter in the book "Relativity and the Dimensionality of the World",
Springer series "Fundamental Theories of Physics", Vol. 153 (2007). Volume
Editor: Vesselin Petko
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