Relativistic Faddeev approach to a non-local NJL model

The diquark and nucleon are studied in a non-local NJL model. We solve the relativistic Faddeev equation and compare the results with the ordinary NJL model. Although the model is quark confining, it is not diquark confining in the rainbow-ladder approximation. We show that the off-shell contribution to the diquark $T$ matrix is crucial for the structure of the nucleon: without its inclusion the attraction in the scalar channel is too weak to form a three-body bound state.Comment: 5 pages (AIP style), 3 figures, Talk presented at the " Xth International Conference on Hadron Spectroscopy (HADRON '03) ", August 31-September 6, 2003, Aschaffenburg, German

Baryon structure in a quark-confining non-local NJL model

We study the nucleon and diquarks in a non-local Nambu-Jona-Lasinio model. For certain parameters the model exhibits quark confinement, in the form of a propagator without real poles. After truncation of the two-body channels to the scalar and axial-vector diquarks, a relativistic Faddeev equation for nucleon bound states is solved in the covariant diquark-quark picture. The dependence of the nucleon mass on diquark masses is studied in detail. We find parameters that lead to a simultaneous reasonable description of pions and nucleons. Both the diquarks contribute attractively to the nucleon mass. Axial-vector diquark correlations are seen to be important, especially in the confining phase of the model. We study the possible implications of quark confinement for the description of the diquarks and the nucleon. In particular, we find that it leads to a more compact nucleon.Comment: 21 pages (RevTeX), 18 figures (eps

A light-front coupled cluster method

A new method for the nonperturbative solution of quantum field theories is described. The method adapts the exponential-operator technique of the standard many-body coupled-cluster method to the Fock-space eigenvalue problem for light-front Hamiltonians. This leads to an effective eigenvalue problem in the valence Fock sector and a set of nonlinear integral equations for the functions that define the exponential operator. The approach avoids at least some of the difficulties associated with the Fock-space truncation usually used.Comment: 8 pages, 1 figure; to appear in the proceedings of LIGHTCONE 2011, 23-27 May 2011, Dalla

The quadratic extension extractor for (hyper)elliptic curves in odd characteristic

We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve C, defined over Fq2, where q is some power of an odd prime. Our extractor, for a given point P on C, outputs the first Fq-coefficient of the abscissa of the point P. We show that if a point P is chosen uniformly at random in C, the element extracted from the point P is indistinguishable from a uniformly random variable in Fq

Predictions for p+p+Pb Collisions at sNN=5\sqrt{s_{NN}} = 5 TeV: Comparison with Data

Predictions made in Albacete {\it et al} prior to the LHC $p+$Pb run at $\sqrt{s_{NN}} = 5$ TeV are compared to currently available data. Some predictions shown here have been updated by including the same experimental cuts as the data. Some additional predictions are also presented, especially for quarkonia, that were provided to the experiments before the data were made public but were too late for the original publication are also shown here.Comment: 55 pages 35 figure

Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach

Renormalization of Hamiltonian field theory is usually a rather painful algebraic or numerical exercise. By combining a method based on the coupled cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian approach to renormalization, we show that a powerful and elegant method exist to solve such problems. The method is in principle non-perturbative, and is not necessarily unitary.Comment: 16 pages, version shortened and improved, references added. To appear in JHE

Scalar Casimir densities for cylindrically symmetric Robin boundaries

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical boundaries. It is assumed that the field obeys general Robin boundary conditions on bounding surfaces. The application of a variant of the generalized Abel-Plana formula allows to extract from the expectation values the contribution from single shells and to present the interference part in terms of exponentially convergent integrals. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. The first one contains well-known surface divergences and needs a further renormalization. The interaction forces between the cylindrical boundaries are finite and are attractive for special cases of Dirichlet and Neumann scalars. For the general Robin case the interaction forces can be both attractive or repulsive depending on the coefficients in the boundary conditions. The total Casimir energy is evaluated by using the zeta function regularization technique. It is shown that it contains a part which is located on bounding surfaces. The formula for the interference part of the surface energy is derived and the energy balance is discussed.Comment: 22 pages, 5 figure

Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell

Vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field are investigated for the geometry of a wedge with a coaxal cylindrical boundary. All boundaries are assumed to be perfectly conducting and both regions inside and outside the shell are considered. By using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of two terms. The first one corresponds to the geometry of the wedge without the cylindrical shell and the second term is induced by the presence of the shell. The vacuum energy density induced by the shell is negative for the interior region and is positive for the exterior region. The asymptotic behavior of the vacuum expectation values are investigated in various limiting cases. It is shown that the vacuum forces acting on the wedge sides due to the presence of the cylindrical boundary are always attractive.Comment: 21 pages, 7 figure

Vacuum energy in conical space with additional boundary conditions

Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit form of the matching conditions depends on the field under consideration. In the case of electromagnetic field, the perfectly conducting boundary conditions or isorefractive matching conditions are imposed on the cylindrical surface. For a massless scalar field, the semi-transparent conditions ($\delta$-potential) on the cylindrical shell are investigated. As a result, the total Casimir energy of electromagnetic field and scalar field, per a unit length along the symmetry axis, proves to be finite unlike the case of an infinitely thin cosmic string. In these studies the spectral zeta functions are widely used. It is shown briefly how to apply this technique for obtaining the asymptotics of the relevant thermodynamical functions in the high temperature limit.Comment: 29 pages, 2 figures, the title was changed for a more adequate one, the abstract was rewritten, a few typos and minor grammar mistakes were correcte