Complex Ashtekar variables and reality conditions for Holst's action

From the Holst action in terms of complex valued Ashtekar variables additional reality conditions mimicking the linear simplicity constraints of spin foam gravity are found. In quantum theory with the results of You and Rovelli we are able to implement these constraints weakly, that is in the sense of Gupta and Bleuler. The resulting kinematical Hilbert space matches the original one of loop quantum gravity, that is for real valued Ashtekar connection. Our result perfectly fit with recent developments of Rovelli and Speziale concerning Lorentz covariance within spin-form gravity.Comment: 24 pages, 2 picture

A gauge model for quantum mechanics on a stratified space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is $\mathrm{SU}(2)$, we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.Comment: 38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been adde

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an $U(1)$ gauge field for which the density is given by a power of the Maxwell Lagrangian. In $d$-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as $d/4$. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking--Page phase transition in spite of conformally invariant Maxwell field.Comment: 13 pages, one figur

White-beaked dolphins trapped in the ice and eaten by polar bears

Polar bears (Ursus maritimus) depend on sea ice, where they hunt ice-associated seals. However, they are opportunistic predators and scavengers with a long list of known prey species. Here we report from a small fjord in Svalbard, Norwegian High Arctic, a sighting of an adult male polar bear preying on two white-beaked dolphins (Lagenorhynchus albirostris) on 23 April 2014. This is the first record of this species as polar bear prey. White-beaked dolphins are frequent visitors to Svalbard waters in summer, but have not previously been reported this far north in early spring. We suggest they were trapped in the ice after strong northerly winds the days before, and possibly killed when forced to surface for air at a small opening in the ice. The bear had consumed most parts of one dolphin. When observed he was in the process of covering the mostly intact second dolphin with snow. Such caching behaviour is generally considered untypical of polar bears. During the following ice-free summer and autumn, at least seven different white-beaked dolphin carcasses were observed in or near the same area. We suggest, based on the area and the degree to which these dolphins had decayed, that they were likely from the same pod and also suffered death due to entrapment in the ice in April. At least six different polar bears were seen scavenging on the carcasses