Regular Series


Vol. 14 (1983), No. 4, pp. 219 – 306


A Relationship Between the Electrovacuum Ernst Equations and Nonlinear \(\sigma \)-Model

abstract

The Ernst equations for the stationary Einstein-Maxwell fields are shown to be connected with the field theory of harmonic map from the Riemann three-space (\(M, h_{ik}\)) into a Kähler symmetric space SU(2,l)/S(U(2)\(\times \)U(l) i.e. the non-linear \(\sigma \)-model on symmetric space of the covariance group of these equations; similarly, the vacuum Ernst equations can be interpreted as the \(\sigma \)-model on SU(l,l)/U(l). The formulation of Ernst’s equations in terms of SU(2,1)-valued field subject to a quadratic constraint, which realizes an embedding of a Kähler symmetric space into the covariance group is given. For the axially symmetric fields it is shown that Ernst’s equations are integrable. The Zakharov–Shabat null-curvature representation of these equations and the corresponding linear system of equations is presented. It is conjectured that an infinite-dimensional group of transformations acting on the solution space of the Ernst equations, which appears naturally in this approach, is connected with the Geroch–Kinnersley group.


Cosmological Character of the Higgs Field

abstract

The Higgs-boson mass in the Weinberg–Salam electroweak theory \(M_H=6.6\) GeV is obtained from the experimental limits on the value of the cosmological constant.


Spin Effects in Hadronic Collisions at Large Momentum Transfers

abstract

The role of spin in hadron-hadron collisions at large \(p_\bot \) is investigated. The short distance diagrams and the end-point \((x \to 1\)) contribution give phenomenologically similar results for the elastic nucleon-nucleon differential cross-section but differ significantly when looking at the spin-spin asymmetries. The spin analysis suggests the dominance of the end-point diagrams at large angles and present energies. The limits on the nucleon wave function are obtained from the comparison of spin effects in exclusive and inclusive reactions. Higher order results in exclusive channels are reviewed. In the inclusive production we propose a simple model of baryon polarization at large transverse momentum which accounts qualitatively for all experimental data in these processes. Other models are also reviewed. The whole investigation suggests that the spin effects are a relatively clear probe of the complicated hadron dynamics.


Failure of a Recently Proposed Q\(\overline {\rm Q}\) Potential to Reproduce Heavy Quarkonium Spectroscopy

abstract

Flory has recently found support for the Shifman, Vainshtein and Zakharov estimate of \(G\) (the density of gluon condensate in Vacuum) by deriving a q–\(\overline {\rm q}\) potential which uses \(G\) as an input and correctly predicts the string tension. Here we show that Flory’s potential gives wrong predictions for energy levels and leptonic widths of quarkonia. Consequently agreement found for the string tension is not conclusive.


Role of the Deformation of Multipolarity Six in the Dynamic Description of Spontaneous Fission

abstract

The role of the deformation of multipolarity six, \(\varepsilon _6\), in the description of spontaneous-fission half-lives is studied. Doubly even heavy nuclei (\(Z=92\)–102) are considered. It is found that inclusion of \(\varepsilon _6\) may change the half-lives by up to about four orders. The structure of the microscopic inertia (mass) tensor, connected with \(\varepsilon _6\), is also investigated. Finally, the equilibrium values of \(\varepsilon _6\) are calculated. It appears that these quantities are of dynamic rather than static nature.


Viscous Cosmological Models with Matter and Radiation

abstract

Robertson–Walker world models filled with interacting matter and radiation, including the bulk viscosity dissipation, are constructed. It is shown that there exist stationary solutions in which the bulk viscosity term can be interpreted as phenomenologically describing a creation of matter and radiation.


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