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Sanchis-Lozano, M. A., Barbero, J. F., & Navarro-Salas, J. (2012). Prime Numbers, Quantum Field Theory and the Goldbach Conjecture. Int. J. Mod. Phys. A, 27(23), 1250136–24pp.
Abstract: Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators b(p)(dagger) – labeled by prime numbers p – acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
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Olmo, G. J., & Rubiera-Garcia, D. (2012). Nonsingular Charged Black Holes A La Palatini. Int. J. Mod. Phys. D, 21(8), 1250067–6pp.
Abstract: We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of general relativity (GR) formulated a la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.
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Oset, E., Ramos, A., Garzon, E. J., Molina, R., Tolos, L., Xiao, C. W., et al. (2012). Interaction of vector mesons with baryons and nuclei. Int. J. Mod. Phys. E, 21(11), 1230011–18pp.
Abstract: After some short introductory remarks on particular issues on the vector mesons in nuclei, in this paper, we present a short review of recent developments concerning the interaction of vector mesons with baryons and with nuclei from a modern perspective using the local hidden gauge formalism for the interaction of vector mesons. We present results for the vector-baryon interaction and in particular for the resonances which appear as composite states, dynamically generated from the interaction of vector mesons with baryons, taking also the mixing of these states with pseudoscalars and baryons into account. We then venture into the charm sector, reporting on hidden charm baryon states around 4400 MeV, generated from the interaction of vector mesons and baryons with charm, which have a strong repercussion on the properties of the J/Psi N interaction. We also address the interaction of K* with nuclei and make suggestions to measure the predicted huge width in the medium by means of transparency ratio. The formalism is extended to study the phenomenon of J/psi suppression in nuclei via J/psi photo-production reactions.
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Dul, M. C., Lescouezec, R., Chamoreau, L. M., Journaux, Y., Carrasco, R., Castellano, M., et al. (2012). Self-assembly, metal binding ability, and magnetic properties of dinickel(II) and dicobalt(II) triple mesocates. CrystEngComm, 14(17), 5639–5648.
Abstract: Two metallacyclic complexes of general formula Na-8[(M2L3)-L-II]center dot xH(2)O [M = Ni (4) and Co (5) with x = 15 (4) and 17 (5)] have been self-assembled in aqueous solution from N,N'-1,3-phenylenebis(oxamic acid) (H4L) and M2+ ions in a ligand/metal molar ratio of 3 : 2 in the presence of NaOH acting as base. X-Ray structural analyses of 4 and 5 show triple-stranded, dinuclear anions of the meso-helicate-type (so-called mesocates) with C-3h molecular symmetry. The two octahedral metal-tris(oxamate) moieties of opposite chiralities (Delta, Lambda form) are connected by three m-phenylene spacers at intermetallic distances of 6.822(2) (4) and 6.868(2) angstrom (5) to give a metallacryptand core. In the crystal lattice, the binding of these heterochiral dinickel(II) and dicobalt(II) triple mesocates to sodium(I) ions leads to oxamato-bridged heterobimetallic three-dimensional open-frameworks with a hexagonal diamond architecture having small pores of 17.566(4) (4) and 17.640(2) angstrom (5) in diameter where the crystallization water molecules and the sodium(I) countercations are hosted. Variable temperature (2.0-300 K) magnetic susceptibility measurements reveal relatively anisotropic S = 2 Ni-2(II) (4) and S = 3 Co-2(II) (5) ground states resulting from the moderate to weak intramolecular ferromagnetic coupling between the two high-spin Ni-II (S-Ni = 1) or Co-II (S-Co = 3/2) ions across the m-phenylenediamidate bridges [J = +3.6 (4) and +1.1 cm(-1) (5); H = -JS(1)center dot S-2]. A simple molecular orbital analysis of the electron exchange interaction identifies the p-type pathways of the meta-substituted phenylene spacers involving the d(z2) and d(x2-y2) pairs of magnetic orbitals of the two trigonally distorted octahedral high-spin M-II ions (M = Ni and Co) as responsible for the overall ferromagnetic coupling observed in 4 and 5 in agreement with a spin polarization mechanism. The decrease of the overall ferromagnetic coupling from 4 to 5 is in turn explained by the additional antiferromagnetic exchange contribution involving the d(xy) pair of magnetic orbitals of the two trigonally distorted octahedral high-spin Co-II ions across the sigma-type pathway of the meta-substituted phenylene spacers.
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Hinarejos, M., Perez, A., & Bañuls, M. C. (2012). Wigner function for a particle in an infinite lattice. New J. Phys., 14, 103009–19pp.
Abstract: We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.
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