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Different types of gauge transformations in gravitation theory are examined in the framework of its fibre bundle reformulation.

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Some known energy-momentum pseudotensors of the gravitational field are considered. On the manifold with the background affine connection these pseudotensors arc tensor functionals of the background connection. Some properties of these functionals are analysed.

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The dynamics of the gravitational field is considered in the affinely connected space. It is shown that the presence of the \(r\)-parameter group of motions of the background connection leads to r integral conservation laws.

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Thermodynamical functions are determined for the bosonic gas distribution in the external gravitational field described by multidimensional cosmological models having the structure \({\rm FRW} \times B^D\), where \(B^D\) is any \(D\)-dimensional compact space with the scalar curvature \(R^{(D)}\). Universal asymptotics of this function are found for the following situations: 1) at high temperatures, with \(\beta ^2R \ll 1\) and \(\beta m_0 \ll 1,\) 2) at low temperatures, with \(\beta ^2R \gg 1\) and \(\beta m_0 \gg 1\), where \(R\) is the scale factor of the physical space, and \(\beta \) is the reciprocal of temperature. It is shown that if \(R^{(3)}/R^{(D)} \gg 1\) (where \(R^{(3)}\) and \(R^{(D)}\) are curvature scalars of macro- and microspace, correspondingly), the Casimir energy is always negative. These results are applied to discuss the dimensional reduction generated by the classical Einstein equations with quantum corrections. The idea of the dynamical dimensional reduction is expressed, in terms of the dynamical system theory, as the problem of the existence of a single stable critical point representing a configuration with the static internal space. It is demonstrated that, in the low-temperature approximation, there is no effective mechanism of the dimensional reduction to a static internal space, if \(B^D\) is a group manifold (with the same scale factor in all internal directions). On the other hand, the effective mechanism of the dimensional reduction to the zero size does exist. The existence of such mechanism for the full class of multidimensional homogeneous cosmologies with the hydrodynamic energy-momentum tensor is also discussed.

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A study of the emission characteristics of secondary particles produced in 340 GeV \(\pi \)-nucleus interactions has been carried to examine some important features of grey particle production obtained experimentally. The values of emission characteristics are compared with the predictions of various models on the dynamics of strong interactions. Results on the multiplicity of relativistic particles are also presented. The values of the mean normalized multiplicity, \(R_A\), estimated in terms of the created charged particles reveal a new kind of scaling in hadron–nucleus interactions at high energies.

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The purpose of this paper is to investigate an influence of space-time topology on the breakdown of chiral symmetry in the model with four-fermion interaction due to formation of fermionic condensate.

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It is shown by the method of functional integration that in the infrared energy region the Green function of the four-fermion model has a simple pole.

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The present paper considers a SU(2)\(_{\rm L} \otimes {\rm U}\)(1)-invariant model with the most general four-fermion interaction of fermions of different generations. It is shown that as a result of dynamic break of symmetry the “upper” fermions (neutrinos) of different generations remain massless whereas the “lower” fermions (leptons e, \(\mu \), \(\tau \) … ) acquire different masses. The spectrum of collective excitations has been found which includes Goldstone fields and fields of massive particles, analogs of Higgs particles representing fermion–antifermion bound states. We have found an effective action of the form similar to the Higgs form, with the difference that for each generation of fermions the mass of the fields, analogs of the Higgs fields, is twice the mass of the fermion.

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A detailed analysis is presented of two \(Z\) production in \(e^+e^-\) annihilation with arbitrary \(ZZ\gamma ^*\) and \(ZZZ^*\) couplings. Both CP-even and CP-odd anomalous couplings are taken into account. The unitarity bounds for the anomalous form factors are found.