[en] Hajj-Boutros's claim [J. Math. Phys. 27, 1592 (1986)] that two new classes of Bianchi type II solutions can be generated from Lorenz's solution [Phys. Lett. A 79, 19 (1980)] is shown to be wrong

[en] It is shown that the class of solutions S-bar(a,0,-1/1), a real slice of the ''complexified'' Plebanski S(a,b,c/m) metrics, is interpretable as colliding wave solutions and, for a = -s₂, coincides precisely with the Ferrari--Ibanez colliding wave metrics

[en] Hamiltonian particle mechanics is formulated on a space-time (M,g). The restrictions imposed by the isometry group G of g on the possible dynamics are analyzed; a no-interaction theorem is obtained on a large class of homogeneous space-times. The results are in particular applied to the de Sitter space-time: here it is proven that a G-invariant dynamics can describe geodesic particle motion only

[en] The extrema of the Euclidean Regge gravitational action are investigated numerically for some closed, compact, four-dimensional simplicial manifolds with topologies S⁴, CP², and S² x S²

[en] The time-independent linear transport problem in a purely absorbing (no scattering) random medium is considered. A formally exact equation for the ensemble averaged distribution function < Psi> is derived. Under the assumption of a two-fluid statistical mixture, with the transition from one fluid to the other assumed to be determined by a Markov process, an exact solution to this equation for < Psi> is obtained. In the source-free case, this solution is shown to agree with the result obtained by ensemble averaging simple exponential attenuation. Several approximations to the exact equation for < Psi> are considered, and numerical results given to assess the accuracy of these approximations

[en] Within the type-D Carter metric structure with a perfect fluid source, it is established that the Wahlquist metric and a new divergenceless solution are the only perfect fluid solutions satisfying positive energy and regularity conditions. The divergenceless solution, obtainable also as a limiting transition of the Wahlquist one, is endowed with three arbitrary parameters, and contains the Kramer fluid solution as a particular case. The fluid four-velocity of these metrics does not lie in the two-space spanned by the double principal null directions of the Weyl tensor

[en] A formalism to study the semiclassical vacuum problem is introduced. Using this formalism we try to satisfy two competitive natural hypotheses: H1, the vacuum definition must assure the absorption of the infinities, coming from the vacuum expectation value of the energy-momentum tensor of the matter fields, in the bare constants of the gravitational classic action; H2, the vacuum must be the ground state. It is proved that the system of equations yielded by these two hypotheses is, in general, incompatible. With this formalism, the vacuum problem in curved space-time is stated. It is hoped that this formalism could eventually be used to solve the problem

[en] The standard definition of space-time perturbation is reexamined. It is seen that the noninvariance of the metric under identification gauge transformations is a consequence of the adopted zero signature in the fifth dimension of the space of space-times. An n-parameter extension of that definition is proposed, with a (4+n)-dimensional flat space of space-times with a nonsingular metric. It is shown that in the vicinity of a point in the background space-time there is a geometrically defined family of perturbations, which are solutions of the Einstein--Yang--Mills equations

[en] An improved ansatz for the three-gluon vertex function is treated; and it is shown that the gluon propagator has a double pole at the origin of the p² plane, as well as a tachyon on the spacelike real axis, at least in this approximation

[en] The self-energy operator for an electron in an external Coulomb potential is investigated analytically using a mass eigenfunction expansion concept reported earlier. Contour integration techniques in the complex m² plane are used to combine bound state and continuum contributions into a single integral. The result is a relatively simple integral representation for the mass operator. Only terms ignoring the ''shift correction'' are considered in this preliminary study. A transformation to a basis of relativistic Coulomb Sturmian functions exhibits the Zα dependence of the integrand in a strikingly simple way. The entire investigation is set in the framework of the ''scalar formalism'' for quantum electrodynamics investigated earlier by a number of authors and based on the ''second-order'' Dirac equation, {Pix(1+iσ)xPi+m²}Phi = 0, where Phi is a 2 x 1 Pauli spinor