Canonical transformation for stiff matter models in quantum cosmology

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.Comment: Revtex4 Class, 3 pages, No Figure

Comparison of solar radio and EUV synoptic limb charts during the present solar maximum

The present solar cycle is particular in many aspects: it had a delayed rising phase, it is the weakest of the last 100 years, and it presents two peaks separated by more than one year. To understand the impact of these characteristics on the solar chromosphere and coronal dynamics, images from a wide wavelength range are needed. In this work we use the 17~GHz radio continuum, formed in the upper chromosphere and the EUV lines 304 and 171~{\AA}, that come from the transition region (He II) and the corona (Fe IX, X), respectively. We analyze daily images at 304 and 171~{\AA} obtained by the Atmospheric Imaging Assembly (AIA). The 17~GHz maps were obtained by the Nobeyama Radioheliograph (NoRH). To construct synoptic limb charts, we calculated the mean emission of delimited limb areas with 100" wide and angular separation of $5^\circ$. At the equatorial region, the results show an hemispheric asymmetry of the solar activity. The northern hemisphere dominance is coincident with the first sunspot number peak, whereas the second peak occurs concurrently with the increase in the activity at the south. The polar emission reflects the presence of coronal holes at both EUV wavelengths, moreover, the 17~GHz polar brightenings can be associated with the coronal holes. Until 2013, both EUV coronal holes and radio polar brightenings were more predominant at the south pole. Since then they have not been apparent in the north, but thus appear in the beginning of 2015 in the south as observed in the synoptic charts. This work strengthens the association between coronal holes and the 17~GHz polar brightenings as it is evident in the synoptic limb charts, in agreement with previous case study papers. The enhancement of the radio brightness in coronal holes is explained by the presence of bright patches closely associated with the presence of intense unipolar magnetic fields.Comment: 6 pages, 5 figures. Acccepted for publication in Astronomy & Astrophysic