[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] Let the compact Lie group G act smoothly on the C/sup infinity/ manifold S with a single orbit type G/H, where H is a closed subgroup of G, and let N(H)/H be a Lie group [N(H) denotes the normalizer of H in G]. Assuming a given connection in the fiber bundle S → M, where M = S/G is the orbit space (to be identified with the physical space-time) and N(H)/H is the structure (gauge) group, the G-invariant tensor fields and linear connections on S are analyzed. A kind of ''dimensional reduction'' for these objects is established: every field corresponds uniquely to a field on M, and the linear connection defines uniquely a set of fields and a linear connection on M

[en] The field equations obtained by Krori, Chaudhury, and Bhattacharjee for Einstein--Dirac--Maxwell fields for several different metrics with a time-independent and a time-dependent Dirac field for a massless neutrino and for a massive neutrino are completely integrated. It is also noted that one of the cases, the particular solutions given by Krori, Chaudhury, and Bhattacharjee, is not correct. All other particular solutions are the special cases of the solutions obtained here

[en] The concept of a Killing--Maxwell system may be defined by the relation A/sub [//sub μ//sub ;//sub v//sub ];//sub rho/ = (4π/3)j/sub [//sub μ/g/sub ν//sub ]/. In such a system the one-form A/sub μ/ is interpretable as the four-potential of an electromagnetic field F/sub μ//sub v/, whose source current j /sup μ/ is an ordinary Killing vector. Such a system determines a canonically associated duality class of source-free electromagnetic fields, its own dual being a Killing--Yano tensor, such as was found by Penrose [Ann. N.Y. Acad. Sci. 224, 125 (1973)] (with Floyd) to underlie the generalized angular momentum conservation law in the Kerr black hole metrics, the existence of the Killing--Yano tensor being also a sufficient condition for that of the Killing--Maxwell system. In the Kerr pure vacuum metric and more generally in the Kerr--Newman metrics for which a member of the associated family of source-free fields is coupled in gravitationally, it is shown that the gauge of the Killing--Maxwell one-form may be chosen so that it is expressible (in the standard Boyer--Lindquist coordinates) by 1/2 (a² cos ² θ-r²)dt+ 1/2 a(r²-a²)sin² θ dphi, the corresponding source current being just (4π/3)(partial/partialt). It is found that this one-form (like that of the standard four-potential for the associated source-free field) satisfies the special requirement for separability of the corresponding coupled charged (scalar or Dirac spinor) wave equations

[en] The method applied by Bellomo and Toscani [J. Math. Phys. 26, 334 (1985)] for the Boltzmann equation in an infinite medium to establish global results for bounded media with partially absorbing boundary conditions is generalized. The method does not require that the equilibrium solution be the vacuum state and, accordingly, does not rely on positivity/monotonicity arguments. The growth produced by the nonlinearity is compensated by the combined effect of streaming and (partial) absorption (leakage) at the boundary

[en] The connection between renormalization schemes (RS's) and the renormalization group (RG) functions for a massive Yang--Mills theory is investigated. The RS's are defined in a manner independent of the regularization procedure. The RS transformations are defined in such a way that it is clear that they form a group. It is shown that to a given set of RG functions corresponds an infinite number of RS's. The subgroup of RS transformations which leave invariant the (mass-shell) MS-RG functions is carefully described. Gauge invariance, regularity of the theory when m→0 and mass decoupling are imposed and the corresponding indeterminations of RS's are given. It is seen that a RS which fulfills simultaneously the above conditions does not exist

[en] The imposition of the condition of length invariance on a Weyl manifold that does not lead uniquely to general relativity is shown. Rather, in this limit, the Weyl vector field can be interpreted as a Dirac current. The action is also the same as the Einstein Dirac one, if and only if, the spinor field is anticommuting. The allowed interactions are greatly restricted. They are only minimal gauge couplings and Yukawa interactions with a scalar field transforming according to the rules of Utiyama [Prog. Theor. Phys. 53, 565 (1975)]

[en] The general spherically symmetric dyonic solutions of vacuum Einstein equations compatible with a K-dimensional toroidal fiber structure in 4+K dimensions are found. Solutions with no electric and/or magnetic change can be obtained by suitable limiting procedures

[en] The anomalies in exceptional-type supersymmetric nonlinear σ models are investigated. The cohomology rings of Kaehler manifolds E₆/Spin(10) x U(1), E₇/SU(5) x SU(3) x U(1), and E₈/SO(10) x SU(3) x U(1) and the Chern classes of the tangent bundles of these manifolds are calculated explicitly. It is shown that the E₆/Spin(10) x U(1) model is anomaly-free but the E₇/SU(5) x SU(3) x U(1) and E₈/SO(10) x SU(3) x U(1) models are anomalous