Quantum Geometry (the modern Loop Quantum Gravity using graphs and spin-networks instead of the loops) provides microscopic degrees of freedom that account for the black-hole entropy. However, the procedure for state counting used in the literature contains an error and the number of the relevant horizon states is underestimated. In our paper a correct method of counting is presented. Our results lead to a revision of the literature of the subject. It turns out that the contribution of spins greater then 1/2 to the entropy is not negligible. Hence, the value of the Barbero-Immirzi parameter involved in the spectra of all the geometric and physical operators in this theory is different than previously derived. Also, the conjectured relation between Quantum Geometry and the black hole quasi-normal modes should be understood again.

but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level. PACS numbers: 4.60.Pp; 04.60.-m; 03.65.Ta; 04.62.+v I. INTRODUCTIONThe recent advances in loop quantum gravity (LQG) [1][2][3][4], strongly suggest that the goal of constructing a candidate for quantum theory of gravity and the Standard Model is within reach. Remarkably, that goal can be addressed within the canonical formulation of the original Einstein's general relativity in four dimensional spacetime. A way to define 'physical' dynamics in a background independent theory, where spacetime diffeomorphisms are treated as a gauge symmetry, is the framework of relational Dirac observables (often also called "partial" observables [5], [6,7],[8] section I.2 of [2]). The main idea is, that part of the fields adopt the role of a dynamically coupled observer, with respect to which the physics of the remaining degrees of freedom in the system is formulated. In this framework the emergence of the dynamics, time and space can be explained as an effect of the relations between the fields. As far as technical issues of a corresponding quantum theory are concerned, the most powerful example of the relational observables framework is the deparametrization technique [9][10][11][12]. This allows to map canonical General Relativity into a theory with a (true) non-vanishing Hamiltonian, that is independent of the (emergent) time provided by the observer fields. All this can be achieved at the classical level, the framework of Loop Quantum Gravity (LQG) itself, provides then the tools of the quantum theory like quantum states, the Hilbert spaces, quantum operators of the geometry and fields and well defined quantum operators for the classical constraints of General Relativity (see [2],[4] and references therein). The combination of LQG with the relational observables and deparametrization framework makes it possible to construct general relativistic quantum models. Applying LQG techniques to perform the quantization step has the consequence that the quantum fields of the Standard Model have to be reintroduced within the scheme of LQG. This is due to the reason that the standard quantum field theory (QFT) defined on the Minkowski (or even ADS) background is incompatible with quantization approach used in LQG. Therefore, the resulting quantum theory of gravity cannot be just coupled to the Standard Model in it's present form. The formulation of the full St...

The polymer quantization of matter fields is a diffeomorphism invariant framework compatible with Loop Quantum Gravity. While studied by itself, it is not explicitly used in the known completely quantizable models of matter coupled to LQG. In the current paper we apply the polymer quantization to the model of massless scalar field coupled to LQG. We show that the polymer Hilbert space of the field degrees of freedom times the LQG Hilbert space of the geometry degrees of freedom admit the quantum constraints of GR and accommodate their explicit solutions. In this way the quantization can be completed. That explicit way of solving the quantum constraints suggests interesting new ideas.

{100}-oriented epitaxial Pb(Zr 0:65 Ti 0:35 )O 3 films with various film thicknesses from 0.1 to 3 m were grown on (100) c SrRuO 3 == (100)SrTiO 3 and (100) c SrRuO 3 == (100)LaNiO 3 == (001)CaF 2 substrates. The out-of-plane/in-plane lattice parameter ratio of the films on the CaF 2 substrates was larger than that on the SrTiO 3 substrates up to 1.1 m film thickness, while (90 À ) ( was defined as the internal tilt angle) was almost 0 .Results of analysis of Raman spectra and piezoresponse images suggest that the 1.1-m-thick film grown on the (100) c SrRuO 3 == (100)LaNiO 3 == (001)CaF 2 substrate had tetragonal symmetry with a polar-axis orientation. Moreover, the saturation polarization values of the films measured from P-E hysteresis loops correspond to the two P s values estimated from the thermodynamic theory, assuming the change in the polar direction due to the symmetry change to tetragonal, and from the crystal distortion in tetragonal symmetry. This can be explained by the large compressive stress from the CaF 2 substrate having a large thermal expansion coefficient. #