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The paper is devoted to the singularity problem in the spatially homogeneous and isotropic cosmology in the framework of the gauge gravitational theory with quadratic gravitational Lagrangian \[L_{\rm g} = \frac {c^4}{16\pi G}({\mit \Omega }^i_{.k} \wedge \eta ^k_i+{\mit \Theta }^i \wedge * {\mit \Theta }_i)+ \frac {\hbar c}{16 \pi } {\mit \Omega }^i_{.k} \wedge * {\mit \Omega }^k_{.i}\,.\]

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Conformal gravity in \(d = 2\) is constructed and discussed with a view to its application in string theory.

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A simple model is described which reproduces qualitative features of the recent data on large transverse energy \((E_{\rm T})\) distributions in proton–Pb collisions at 200 GeV/\(c\) obtained by the HELIOS collaboration at CERN. The same model is used to predict the \(E_{\rm T}\) distributions in \(^{16}\)O–\(^{238}\)U collisions. The model is based on the assumption that each of the wounded constituents (nucleons or quarks) in the nucleus gives rise to a “string” in the target fragmentation region. Both the number of “strings” and the number of soft hadron pairs produced from a single string within a given rapidity interval are assumed to be Poisson distributed stochastic quantities. The total \(E_{\rm T}\) is assumed to be built up by contributions of soft hadrons. We argue that the signature of plasma formation could be seen as an excess of events above the model predictions in the large \(E_{\rm T}\) tail of the \(E_{\rm T}\)-distributions.

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This is a review of some recent work in which a derivative expansion technique is used to calculate terms in an effective Lagrangian, starting from some more fundamental Lagrangian.

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An elementary discussion is given of the mechanism whereby the Wess–Zumino et al. is drawn upon to make explicit the remark of Wu and Zee that the Wess–Zumino term acts like a monopole in the space, of scalar fields of the non-linear \(\sigma \)-model. The origin of the monopole structure, and its influence on quantization, is discussed in terms of the Berry (adiabatic) phase.

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Effective action for the \(\lambda \phi ^4\) theory and scalar electrodynamics interacting in nonminimal way with the curvature and torsion in the de Sitter space is calculated. It is shown that torsion which was absent at the classical level is induced as a result of quantum corrections. The possibility of a first-order phase transition induced by curvature and torsion in scalar electrodynamics is investigated.

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It is shown that the supersymmetry algebra for massive free fields has to contain the translations — the absence of translations implies vanishing of supersymmetry altogether.

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We present first results of the analysis carried in our laboratories on the 800 GeV proton-emulsion data obtained from the Fermi National Accelerator Laboratory experiment No. 508. The multiplicity distributions of secondary particles and the pseudorapidity distribution of shower particles are analyzed and compared with those obtained at lower energies.

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In the paper, a relation between the Hill–Wheeler integral and the angular momentum lowering operator is derived and used to construct the orthonormal physical basis for the Bohr-type and IBM collective Hamiltonians.