abstract

A unified description of the gravitational and gauge fields in terms of a metric tensor and a linear connection on the bundle manifold is proposed. It is pointed out that the Lagrangian should contain, except of the Ricci scalar term, an additional term quadratic in torsion.

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We consider a four dimensional Lorentzian space-time (\(V_4\), \(g\)) which admits a \(S_2\) separability structure and we investigate the algebraic classification of its Weyl tensor. We show that \(S_2\) separability does not impose algebraic restrictions on the Weyl tensor of (\(V_4\), \(g\)) or in other words empty space-time of any Petrov type could admit the \(S_2\) separability structure.

abstract

Diffraction Glauber theory for nucleus–nucleus collisions is considered in approximation when the initial nucleus interacts as a whole with nucleons of the target nucleus. Such an approach, being intermediate between precise Glauber theory and its optical limit, essentially simplifies numerical calculations and gives a good agreement with experiments as well.

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Quasi-classical approximation is used to describe heavy nuclei interactions near the Coulomb barrier. The relative motion of colliding nuclei occurs not along geometric optics straight paths, as is the case in the high energy region, but along the curved Coulomb trajectories. The influence of this effect is considered.

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This paper is concerned with the study of the SL(2,\(R\)) group as a hadronic mass-group group, one of whose generators is the mass squared operator \(M^2\)). It is shown that, besides dual models, also conformal invariant quantum field models admit SL(2,\(R\)) as a mass-group. The mass-algebra is explicitly constructed and its representation on the field derived. The separation between kinematical and dynamical degrees of freedom results from the construction and the dynamical content of the theory is shown to be specified by the choice of unitary, irreducible representations of the mass-group appearing in the spectrum. The problem of interpreting the modular group invariance of dual mass-spectra is considered from the point of view of breakdown of SL(2,\(R\)) mass-group and a no-go theorem is proved. Therefore it is shown that the physical interpretation of the modular group in hadron physics must be indirect, in the sense that it is the shadow, on the 2-point function, of another, so far, hidden symmetry.

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An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts.

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An analysis of the data on \(\rho \) and \(\psi \) trajectories is carried out. In the framework of a model with square-root asymptotics both trajectories have asymptotically the same slope. This slope is determined by the \(\pi \)-meson radius. The leading thresholds for \(\rho \) and \(\psi \), trajectories are disposed at \(\sqrt {s} \simeq 2.4\) and 4.9 GeV, respectively.

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It is suggested in this note that the \(\psi ^{\prime \prime }\)(3770) must have \(I^G=0^-\).

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The relativistic radial equations for two spin-l/2 particles, consistent with the hole theory, are derived from the one-time Salpeter equation. They may be of much help in relativistic calculations for leptonium and quarkonium.

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We argue that the conventional approach to the infrared catastrophe with a very small resolution energy with respect to the rest electron mass is not convenient for large energies. We conjecture that for the high energy QED it is better to consider the semi-inclusive (or inclusive) scattering. This scattering has the positive cross section and is relativistically invariant. It is shown by the explicit calculations that to the fourth and sixth orders of the Coulomb scattering in the Born approximation, leading logarithms can be obtained treating formally the real photons as the soft photons. Conjecturing that this is true for higher orders of perturbation theory and summing an infinite set of diagrams, we obtain the anomalous dimension, which is a function of the coupling constant only. We calculate the cross sections for the electron–electron and electron-proton scattering showing that the anomalous dimension does not depend upon the statistical correlation of the final particles.

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The question of compatibility of the MIT bag model with standard chiral symmetry breaking is investigated in the (3,\(\overline {3}\))\(\oplus \)(\(\overline {3}\),3) model. We find that the chiral symmetry breaking parameter \(c\) is given by \(c = -0.79\) and compute the meson and baryon \(\sigma \) terms in the bag model. For example, in case of the \(\pi \)N scattering a term, we obtain 104 MeV.

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It is pointed out that experimental data on the \(A\)-dependence of the average multiplicity of produced particles in \(\overline {\rm p}\)-nucleus collisions and/or on the number of leading protons in p-nucleus collisions, could be used to eliminate some of the competing models of hadron–nucleus scattering.