abstract

We begin with the presentation of the well known method used in classical mechanics for purpose of extending the Galilei group centrally. We show then that it is not possible to carry over this method mutatis mutandis to the case of classical scalar fields and relativistic transformations like Poincaré, Lorentz and translational groups.

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We briefly overview the development of Euclidean quantum gravity in four dimensions regarded as a branch of statistical mechanics of discretized random manifolds.

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In theoretical physics, one often considers symmetries which change a Lagrangian by a total divergence. Such transformations preserve the equations of motion and lead to conservation laws. It is argued here, on the basis of a few examples, that the appearance of such a divergence is an indication that one is dealing with some approximation or a limiting case of a “better” theory, in which the corresponding, possibly modified, symmetries fully preserve the action integral. These suggestions are “metaphysical” in the sense that they cannot be tested by physical experiments.

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Firstly, we show how fundamental masses (Planck mass, string mass) appear as a feature of quantum gravity as well as in fundamental string theory. Further, we use the classical \(r\)-matrix approach for the description of the lowest order quantum deformations. We provide relevant examples of \(D=4\) Poincaré and \(D=4\) conformal bialgebras which introduce fundamental masses as deformation parameters.

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For \(m_{\rm top}\gt 150\) GeV there exists an \((m_{\rm top}\), \(m_{\rm Higgs})\)-area in which both the SM and the MSSM are excluded. But the requirement of vacuum stability in a 2-Higgs model fits into this region. With supersymmetric SU(5) one can overcome by part the so-called hierarchy problem. Further, SU(5) and SO(10) supersymmetric GUT models with fixed point solutions and non-linear realizations of SUSY belong also to this area. Finally, one can show that the SM originates from its minimal supersymmetric extension which is explicitely broken due to soft SUSY breaking terms at scale \(M_{\rm SUSY}\), and that the NMSSM has roughly no influence on the previous predictions. So far the discovery of Top at FNAL “localizes” Higgs.

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We show that there is a choice of the gauge condition such that the mixed problem for the Hamiltonian form of the evolution equations for Yang–Mills fields in spatially bounded domains (with inhomogeneous boundary conditions) admits the finite time existence and uniqueness of solutions.

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The perturbative QCD predictions for the small \(x\) behaviour of the nucleon structure functions \(F_{2,L}(x, Q^2)\) and \(g_1(x, Q^2)\) are summarized. The importance of the double logarithmic terms for the small \(x\) behaviour of the spin structure function \(g_1(x, Q^2)\) is emphasized. These terms correspond to the contributions containing the leading powers of \(\alpha _s\) ln\(^2(1/x)\) at each order of the perturbative expansion. In the non-singlet case they can be approximately accounted for by the ladder diagrams with quark (antiquark) exchange. We solve the corresponding integral equation with the running coupling effects taken into account and present estimate of the effective slope controlling the small \(x\) behaviour of the non-singlet spin structure function \(g_1(x, Q^2)\) of a nucleon.

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A fit to proton, neutron and deuteron spin asymmetries is presented and polarized parton distributions in nucleon are given. These densities have their roots in the MRS fit for unpolarized case. The integrals of polarized distributions are compared with the experimental figures. The role of polarized gluons is also discussed.

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The process of top quark pair production at Next Linear Collider (NLC) has been considered adopting an effective Lagrangian approach and including all operators of dim 6 which can be tree-level-generated within unknown underlying theory. All contributing helicity amplitudes are presented. It has been found that four-fermion operators can provide the leading non-standard contribution to the total cross section. Expected statistical significance of the non-standard signal for the total cross section and forward-backward asymmetry have been calculated taking into account existing experimental constraints. It has been shown that adopting realistic luminosity of NLC and conservative efficiency for the top-quark pair detection, the total cross section may be sensitive to non-standard physics of an energy scale around \({\mit \Lambda }=5\) TeV.

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The fits to the recent precision electroweak LEP1 data and measurement of \(M_W\) are presented. We analyze the impact different measurements have on the Higgs boson mass bounds extracted from such fits.

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Some properties of pionium are studied. The decay width in the 1s state is related to the scattering lengths. Chances to produce pionium in hadron–hadron collisions are calculated. Special attention is paid to the effects of an external Coulomb field on the atomic formation process. Corrections to the coalescence model are found and the rate of 2p state production due to the external field is calculated.

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We investigate the production of Higgs bosons \(A/h\) via the Yukawa process \(Z \to f \bar f\,A/h\) taking into account QCD corrections and fermion mass effects. We estimate the discovery reach of this process and/or bounds on the parameter space of two-Higgs doublet models which can be derived from the analysis of \(b \bar b \tau ^+\tau ^-\) events at LEP1. These limits have important consequences for extended models of electroweak interactions and their experimental verification/improvement are welcome.

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We count the number of CP breaking phases in models with SU(2)\(_L \times \) U(1)\(_Y\) and SU(2)\(_L \times \) SU(2)\(_R \times \) U(1)\(_{B-L}\) electroweak gauge groups and extended matter contents with some fermion masses vanishing and/or degenerate. Quarks and leptons, including Majorana neutrinos, are treated in a similar way. CP violation is characterized in the mass-eigenstate and in the weak-eigenstate bases. Necessary and sufficient conditions for CP conservation, invariant under weak basis redefinitions are also studied in these models. CP violating factors entering in physical observables and only invariant under phase redefinitions are discussed.

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The theory of the inclusive \((K^-,\pi ^+)\) reaction, in which only the pion spectrum is measured, is presented. The hyperon in the final state — either \({\mit \Sigma }^-\) or \({\mit \Lambda }\) (produced via \({\mit \Sigma \Lambda }\) conversion) — is described in the effective two-channel approach, and the cross section is calculated in the coupled-channels impulse approximation. The theory is applied to the \((K^-,\pi ^+)\) reaction on the \(^{16}\)O target and compared with existing data.

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Assignments for the configurations underlying the formation of identical bands in terms of the eigenstates of rotating harmonic oscillator are discussed in superdeformed nuclei. The method which is based on the pseudo-SU(3) symmetry is applied to the superdeformed bands in nuclei from the \(A \sim 130\) region.

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Nuclear masses of heaviest nuclei are studied theoretically within a macroscopic–microscopic approximation. Effect of various approaches to the macroscopic part of the mass on the quality of description of already known masses, and also on the masses of nuclei expected to be synthesized in a near future, is analyzed. Even–even nuclei with proton number \(Z=82\)–116 and neutron number \(N=126\)–176 are considered.

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It is shown that quantum fluctuations due to a nontrivial gravitational background in the flat radiation dominated universe can play an important cosmological role generating nonvanishing cosmological global charge, e.g. baryon number, asymmetry. The explicit form of the fluctuations at vacuum and at finite temperature is given. Implications for particle physics are discussed.