Effective action and semiclassical limit of spin foam models

We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam effective action if the vertex amplitude has the large-spin asymptotics which is proportional to an exponential function of the vertex Regge action. In the case of the known three-dimensional and four-dimensional spin foam models this amounts to modifying the vertex amplitude such that the exponential asymptotics is obtained. In particular, we show that the ELPR/FK model vertex amplitude can be modified such that the new model is finite and has the Einstein-Hilbert action as its classical limit. We also calculate the first-order and some of the second-order quantum corrections in the semi-classical expansion of the effective action.Comment: Improved presentation, 2 references added. 15 pages, no figure

FLOTATION KINETICS OF MAGNESIUM HYDROXIDE SEDIMENTED FROM SEA WATER

Synthetic sea water has been taken as a referential sample, in which Mg(OH)2 had been sedimented, in order to reduce biological effects and confirm reproducibility of results of the familiar composition sample. The synthetic sea water was prepared according to the scientifically developed procedure. Flotation experiments were performed in the apparatus for flotation under pressure and recoveries of floated Mg(OH)2 were determined depending on the time of flotation. The results obtained on the referential sample of the synthetic water were also tested on the sample of natural sea water and presented comparatively during work. Flotation kinetics is in most cases described by an equation of the first or second degree. However, it was established that flotation kinetics of Mg(OH)2 as chemical sediment with both types of prepared magnesium hydroxide suspension, sedimented in both the synthetic and natural sea water corresponded to the velocity of reaction n = 1.5 degree, which fully corresponds to Horst Morris’s theoretical postulates in the theory of flotation kinetics

FLOTATION KINETICS OF MAGNESIUM HYDROXIDE SEDIMENTED FROM SEA WATER

Synthetic sea water has been taken as a referential sample, in which Mg(OH)2 had been sedimented, in order to reduce biological effects and confirm reproducibility of results of the familiar composition sample. The synthetic sea water was prepared according to the scientifically developed procedure. Flotation experiments were performed in the apparatus for flotation under pressure and recoveries of floated Mg(OH)2 were determined depending on the time of flotation. The results obtained on the referential sample of the synthetic water were also tested on the sample of natural sea water and presented comparatively during work. Flotation kinetics is in most cases described by an equation of the first or second degree. However, it was established that flotation kinetics of Mg(OH)2 as chemical sediment with both types of prepared magnesium hydroxide suspension, sedimented in both the synthetic and natural sea water corresponded to the velocity of reaction n = 1.5 degree, which fully corresponds to Horst Morris’s theoretical postulates in the theory of flotation kinetics

A finiteness bound for the EPRL/FK spin foam model

We show that the EPRL/FK spin foam model of quantum gravity has an absolutely convergent partition function if the vertex amplitude is divided by an appropriate power $p$ of the product of dimensions of the vertex spins. This power is independent of the spin foam 2-complex and we find that $p>2$ insures the convergence of the state sum. Determining the convergence of the state sum for the values $0 \le p \le 2$ requires the knowledge of the large-spin asymptotics of the vertex amplitude in the cases when some of the vertex spins are large and other are small.Comment: v6: published versio

Classical String in Curved Backgrounds

The Mathisson-Papapetrou method is originally used for derivation of the particle world line equation from the covariant conservation of its stress-energy tensor. We generalize this method to extended objects, such as a string. Without specifying the type of matter the string is made of, we obtain both the equations of motion and boundary conditions of the string. The world sheet equations turn out to be more general than the familiar minimal surface equations. In particular, they depend on the internal structure of the string. The relevant cases are classified by examining canonical forms of the effective 2-dimensional stress-energy tensor. The case of homogeneously distributed matter with the tension that equals its mass density is shown to define the familiar Nambu-Goto dynamics. The other three cases include physically relevant massive and massless strings, and unphysical tahyonic strings.Comment: 12 pages, REVTeX 4. Added a note and one referenc

Poincare 2-group and quantum gravity

We show that General Relativity can be formulated as a constrained topological theory for flat 2-connections associated to the Poincar\'e 2-group. Matter can be consistently coupled to gravity in this formulation. We also show that the edge lengths of the spacetime manifold triangulation arise as the basic variables in the path-integral quantization, while the state-sum amplitude is an evaluation of a colored 3-complex, in agreement with the category theory results. A 3-complex amplitude for Euclidean quantum gravity is proposed.Comment: v3: published versio

Association of common genetic variants with brain microbleeds

OBJECTIVE: To identify common genetic variants associated with the presence of brain microbleeds (BMBs). METHODS: We performed geno

EU enlargement and real economic convergence

This article presents an analysis of economic implications of the major EU enlargement in 2004. The research is based on sigma (σ) and beta (β) convergence of per capita GDP among the 10 countries which joined the European Union in 2004. Our results confirm the existence of both types of convergence in the second half of the 1990s and the 2000s. Generally, the poorer new EU member states grew faster than the richer new EU member states. As a result, the income gap between these two groups of countries has narrowed although it still remains quite large. The convergence occurred at the rate of 4.2% during the period 1992–2006 and 7.0% and 9.6% during the sub-periods 1995–2006 and 2002–06 respectively.