Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC

A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts.Comment: RevTex4, 32 page

Parameters of scalar resonances from the combined analysis of data on processes ππ→ππ,KKˉ,ηη\pi\pi\to\pi\pi,K\bar{K},\eta\eta and J/ψJ/\psi decays

A combined analysis of data on isoscalar S-wave processes $\pi\pi\to\pi\pi,K\overline{K},\eta\eta$ and on decays $J/\psi\to\phi\pi\pi,\phi K\overline{K}$ from the DM2, Mark III and BESIII collaborations is performed to study $f_0$ mesons. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. In the analysis limited only to the multi-channel $\pi\pi$-scattering data, two possible sets of parameters of the $f_0(500)$ were found: in both cases the mass was about 700 MeV but the total width was either about 600 or 930 MeV. The extension of the analysis using only the DM2 and Mark III data on the $J/\psi$ decays does not allow to choose between these sets. However, the data from BESIII on the di-pion mass distribution in the decay $J/\psi\to\phi\pi^+\pi^-$ clearly prefers the wider $f_0(500)$ state. Spectroscopic implications from results of the analysis are also discussed.Comment: the formalism is also described (text overlap) in arXiv:1108.3725; new extended analysis of data; revised PRD versio

Background independent quantizations: the scalar field II

We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the `quantum' polymer *-star algebra and looking for positive linear functionals, called states. Assumed in our paper homeomorphism invariance allows to derive the complete class of the states. They are determined by the homeomorphism invariant states defined on the CW-complex *-algebra. The corresponding GNS representations of the polymer *-algebra and their self-adjoint extensions are derived, the equivalence classes are found and invariant subspaces characterized. In the preceding letter (the part I) we outlined those results. Here, we present the technical details.Comment: 51 pages, LaTeX, no figures, revised versio

Background independent quantizations: the scalar field I

We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the `quantum' polymer *-star algebra and looking for positive linear functionals, called states. The assumed in our paper homeomorphism invariance allows to determine a complete class of the states. Except one, all of them are new. In this letter we outline the main steps and conclusions, and present the results: the GNS representations, characterization of those states which lead to essentially self adjoint momentum operators (unbounded), identification of the equivalence classes of the representations as well as of the irreducible ones. The algebra and topology of the problem, the derivation, all the technical details and more are contained in the paper-part II.Comment: 13 pages, minor corrections were made in the revised versio

Juvenile tench ( Tinca tinca L.) response to practical diets with different replacement levels of fish meal by pea protein concentrate supplemented with methionine

.The effects of methionine supplementation in diets with different replacement levels of fish meal (FM) by pea protein concentrate (PPC) on survival, growth performance and body composition of juvenile tench (0.39 g of initial weight) were studied in a 90-day experiment. Six practical diets (50% crude protein) differing in replacement level of FM by PPC were tested: 0% (control diet), 35%,45%, 60%, 75% or 85%, corresponding to 0, 285, 366, 487, 608 and 685.4 g PPC kg−1 diet respectively. To provide the same amount as in control diet, methionine was included from the 45% substitution level. Survival rates were high, between 93.7% and 100%, without differences among treatments. Juveniles fed 75% and 85% of replacement diets showed lower (p < 0.05) weight and specific growth rate, which cannot be attributed to methionine deficiency. In all treatments, percentages of fish with externally visible deformities were low (under 0.1%). The increase in PPC diet content resulted in a significant reduction of lipid content in whole-body juvenile. Minimum methionine requirements for juvenile tench could be estimated in 10 g kg−1 diet and supplementation over this amount would be not necessary. Juvenile tench exhibited a high tolerance to PPC dietary content, up to 487 g kg−1, without affecting growth performance, which make possible to consider this vegetal source of protein as a suitable substitute to FM.S

Representations of the Weyl Algebra in Quantum Geometry

The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A having a cyclic and diffeomorphism invariant vector, is already unitarily equivalent to the fundamental representation. Additional assumptions concern the dimension of the underlying analytic manifold (at least three), the finite wide triangulizability of surfaces in it to be used for the fluxes and the naturality of the action of diffeomorphisms -- but neither any domain properties of the represented Weyl operators nor the requirement that the diffeomorphisms act by pull-backs. For this, the general behaviour of C*-algebras generated by continuous functions and pull-backs of homeomorphisms, as well as the properties of stratified analytic diffeomorphisms are studied. Additionally, the paper includes also a short and direct proof of the irreducibility of A.Comment: 71 pages, 1 figure, LaTeX. Changes v2 to v3: previous results unchanged; some addings: inclusion of gauge transforms, several comments, Subsects. 1.5, 3.7, 3.8; comparison with LOST paper moved to Introduction; Def. 2.5 modified; some typos corrected; Refs. updated. Article now as accepted by Commun. Math. Phy

The Plebanski sectors of the EPRL vertex

Modern spin-foam models of four dimensional gravity are based on a discrete version of the $Spin(4)$ Plebanski formulation. Beyond what is already in the literature, we clarify the meaning of different Plebanski sectors in this classical discrete model. We show that the linearized simplicity constraints used in the EPRL and FK models are not sufficient to impose a restriction to a single Plebanski sector, but rather, three Plebanski sectors are mixed. We propose this as the reason for certain extra `undesired' terms in the asymptotics of the EPRL vertex analyzed by Barrett et al. This explanation for the extra terms is new and different from that sometimes offered in the spin-foam literature thus far.Comment: 17 page

ππ\pi\pi scattering S wave from the data on the reaction π−p→π0π0n\pi^-p\to\pi^0\pi^0n

The results of the recent experiments on the reaction $\pi^-p\to\pi^0\pi^0n$ performed at KEK, BNL, IHEP, and CERN are analyzed in detail. For the I=0 $\pi\pi$ S wave phase shift $\delta^0_0$ and inelasticity $\eta^0_0$ a new set of data is obtained. Difficulties emerging when using the physical solutions for the $\pi^0\pi^0$ S and D wave amplitudes extracted with the partial wave analyses are discussed. Attention is drawn to the fact that, for the $\pi^0\pi^0$ invariant mass, m, above 1 GeV, the other solutions, in principle, are found to be more preferred. For clarifying the situation and further studying the $f_0(980)$ resonance thorough experimental investigations of the reaction $\pi^-p\to\pi^0\pi^0n$ in the m region near the $K\bar K$ threshold are required.Comment: 17 pages, 5 figure