Degeneracies when T=0 Two Body Interacting Matrix Elements are Set Equal to Zero : Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle

In a previous work we studied the effects of setting all two body T=0 matrix elements to zero in shell model calculations for $^{43}$Ti ($^{43}$Sc) and $^{44}$Ti. The results for $^{44}$Ti were surprisingly good despite the severity of this approximation. In this approximation degeneracies arose in the T=1/2 I=$({1/2})^-_1$ and $({13/2})^-_1$ states in $^{43}$Sc and the T=1/2 $I=({13/2})_2^-$, $({17/2})^-_1$, and $({19/2})_1^-$ in $^{43}$Sc. The T=0 $3_2^+$, $7_2^+$, $9_1^+$, and $10_1^+$ states in $^{44}$Ti were degenerate as well. The degeneracies can be explained by certain 6j symbols and 9j symbols either vanishing or being equal as indeed they are. Previously we used Regge symmetries of 6j symbols to explain these degeneracies. In this work a simpler more physical method is used. This is Talmi's method of calculating coefficients of fractional parentage for identical particles to states which are forbidden by the Pauli principle. This is done for both one particle cfp to handle 6j symbols and two particle cfp to handle 9j symbols. The states can be classified by the dual quantum numbers ($J_{\pi},J_{\nu}$)

Exclusive electromagnetic production of strangeness on the nucleon : review of recent data in a Regge approach

In view of the numerous experimental results recently released, we provide in this letter an update on the performance of our simple Regge model for strangeness electroproduction on the nucleon. Without refitting any parameters, a decent description of all measured observables and channels is achieved. We also give predictions for spin transfer observables, recently measured at Jefferson Lab which have high sensitivity to discriminate between different theoretical approaches.Comment: 5 pages, 5 figure

Tetraquark spectroscopy

A complete classification of tetraquark states in terms of the spin-flavor, color and spatial degrees of freedom was constructed. The permutational symmetry properties of both the spin-flavor and orbital parts of the quark-quark and antiquark-antiquark subsystems are discussed. This complete classification is general and model-independent, and is useful both for model-builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a definite dynamical model. This is also valid for diquark-antidiquark models, for which the basis is a subset of the one we have constructed. An evaluation of the tetraquark spectrum is obtained from the Iachello mass formula for normal mesons, here generalized to tetraquark systems. This mass formula is a generalizazion of the Gell-Mann Okubo mass formula, whose coefficients have been upgraded by means of the latest PDG data. The ground state tetraquark nonet was identified with $f_{0}(600)$, $\kappa(800)$, $f_{0}(980)$, $a_{0}(980)$. The mass splittings predicted by this mass formula are compared to the KLOE, Fermilab E791 and BES experimental data. The diquark-antidiquark limit was also studied.Comment: Invited talk at 11th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2007), Julich, Germany, 10-14 Sep 2007. In the Proceedings of 11th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2007), Julich, Germany, 10-14 Sep 2007, eConf C070910, 163 (2007

Invariants of 2+1 Quantum Gravity

In [1,2] we established and discussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genus $g$ with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to $6g-6 (g > 1)$ is treated in detail with a precise classification for $g = 1$ and $g = 2$.Comment: 10 pages, plain TEX, no figures, DFTT 46/9

Finite size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T=0 critical point.Comment: Latex with 3 ps figures. Last versio

An Uncertainty Relation of Space-Time

We propose an uncertainty relation of space-time. This relation is characterized by GhT \lesssim \delta V, where T and \delta V denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of 't Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic principle of Fischler and Susskind. However, as for the maximal entropy of a system with an energy E, we obtain the formula \sqrt{EV/Gh^2}, with V denoting the volume of the system, which is distinct from the Bekenstein entropy formula ER/h with R denoting the length scale of the system.Comment: 13 pages, Journal Version, PTPTe

Black Holes in Three Dimensional Topological Gravity

We investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and compare with results obtained in Einstein gravity. We find that the theory with topological matter reverses the identification of energy and angular momentum with the parameters in the metric, compared with general relativity, and that the entropy is determined by the circumference of the inner rather than the outer horizon. We speculate that this results from the contribution of the topological matter fields to the conserved currents. We also briefly discuss two new possible (2+1)-dimensional black holes.Comment: 14 pages, LateX, UNB Tech. Rep. 94-03, UCD- 94-3

Oddballs and a Low Odderon Intercept

We report an odderon Regge trajectory emerging from a field theoretical Coulomb gauge QCD model for the odd signature JPC (P=C= -1) glueball states (oddballs). The trajectory intercept is clearly smaller than the pomeron and even the omega trajectory's intercept which provides an explanation for the nonobservation of the odderon in high energy scattering data. To further support this result we compare to glueball lattice data and also perform calculations with an alternative model based upon an exact Hamiltonian diagonalization for three constituent gluons.Comment: 4 pages, 2 figures, 1 tabl

Pair creation of higher dimensional black holes on a de Sitter background

We study in detail the quantum process in which a pair of black holes is created in a higher D-dimensional de Sitter (dS) background. The energy to materialize and accelerate the pair comes from the positive cosmological constant. The instantons that describe the process are obtained from the Tangherlini black hole solutions. Our pair creation rates reduce to the pair creation rate for Reissner-Nordstrom-dS solutions when D=4. Pair creation of black holes in the dS background becomes less suppressed when the dimension of the spacetime increases. The dS space is the only background in which we can discuss analytically the pair creation process of higher dimensional black holes, since the C-metric and the Ernst solutions, that describe respectively a pair accelerated by a string and by an electromagnetic field, are not know yet in a higher dimensional spacetime.Comment: 10 pages; 1 figure included; RexTeX4. v2: References added. Published version. v3: Typo in equation (46) fixe