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 $\phi$ and its canonical moment $L_{z}$. 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 $\varepsilon$ for the scale factor in the matter dominated era of the form $t^{\frac{2}{3}+\varepsilon}$. Based on recent $H(z)$ data, the best fit values for the mass of dark matter created particles and the $\varepsilon$ parameter have been found as $m=1.6\times10^3$ GeV, restricted to a 68.3\% c.l. interval of ($1.5<m<6.3\times10^7$) GeV and $\varepsilon = -0.250^{+0.15}_{-0.096}$ 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