By studying multidimensional Kaluza-Klein theories, or gravity plus U(1) or SU(2) gauge fields it is shown that these theories possess similar flux tube solutions. The gauge field which fills the tube geometry of these solutions leads to a comparision with the flux tube structures in QCD. These solutions also carry a "magnetic" charge, Q, which for the SU(2) Einstein-Yang-Mills (EYM) system exhibits a dual relationship with the Yang-Mills gauge coupling, g, (Q = 1/g). As Q → 0 or Q → ∞, g → ∞ or g → 0 respectively. Thus within this classical EYM field theory we find solutions which have features -flux tubes, magnetic charges, large value of the gauge coupling -that are similar to the key ingredients of confinement in QCD

We consider a D-dimensional self-gravitating spherically symmetric configuration of a generalized electro-magnetic n-form F and a dilatonic scalar field, admitting an interpretation in terms of intersecting p-branes. For theories with multiple times, selection rules are obtained, which obstruct the existence of p-branes in certain subspaces. General static solutions are obtained under a specific restriction on the model parameters, which corresponds to the known "intersection rules". More special families of solutions (with equal charges for some of the F -field components) are found with weakened restrictions on the input parameters. Black-hole solutions are determined, and it is shown that in the extreme limit the Hawking temperature may tend to zero, a finite value, or infinity, depending on the p-brane intersection dimension. A kind of no-hair theorem is obtained, claiming that black holes cannot coexist with a quasiscalar component of the F -field.

The author compares the methods proposed by Boulware (1984), and Buchbinder and Lyachovich (1987), to establish a Hamiltonian formalism for fourth-order gravity and studies another possibility to circumvent second-order derivatives of the metric tensor components on the level of the Lagrangian for fourth-order theories of gravity, by introduction of a scalar field. This is done in a way different from the common procedure of doing a conformal transformation of the metric. It is demonstrated how the well known fourth-order field equations result. On the basis of the Hamiltonian formalism, the author considers the quantum cosmology for homogeneous and isotropic closed models. As a first application, the WKB approximation is discussed neglecting the spatial curvature. Chosen initial conditions have the consequence that the resulting wavefunction leads to the inflationary stage of the cosmic evolution.

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We consider a D-dimensional cosmological model describing an evolution of (n + 1) Einstein factor spaces (n ≥ 2) in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system. We consider the case, when characteristic vectors of the model, related to p-branes configuration and their couplings to the dilatonic fields, may be interpreted as the root vectors of a Lie algebra of the type Am. The model is reduced to the open Toda chain and integrated. The exact solution is presented in the Kasner-like form.