Problems and strategy of the first flight to the comets

Substantiation is given for the urgency of using space equipment to study comets in order to work out the basic problem of the origin and evolution of the solar system. The potentialities and advantages of selecting ballistically-accessible objects among the newly discovered comets are shown (as a preliminary study). The technique of early detection of such objects is discussed

On the Question of Polygonality and Irregularities of the Shape of Certain Craters on the Moon

Evaluation of moon crater polygonality, and irregular shape

Penetrators (penetrating sondes) and new possibilities for study of the planets

The fields of possible use of penetrators in space research are considered. A survey of the condition of development and plans for use of penetrators abroad is presented and an analysis is given of the significance of scientific problems when probing planets

Yang-Mills condensates in cosmology

We discuss homogeneous and isotropic cosmological models driven by SU(2) gauge fields in the framework of Einstein gravity. There exists a Yang-Mills field configuration, parametrized by a single scalar function, which consists of parallel electric and magnetic fields and has the stress tensor mimicking an homogeneous and isotropic fluid. The unique SU(2) gauge theory with spontaneous symmetry breaking sharing the same property is the Yang-Mills coupled to the complex doublet Higgs, this exists only in the case of the closed universe. This model contains an intrinsic mechanism for inflation due to the Higgs potential. Our second goal is to show that a successful inflation can be achieved also within the pure Yang-Mills theory adding an appropriate theta-term.Comment: Submitted to Proceedings of "Quantum field theory under the influence of external conditions", Benasque, Spain, September 18-24, 2011 2011, Sep 18 -- Sep 2

Cylindrically symmetric solitons in Einstein-Yang-Mills theory

Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_\phi$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on the parameters, the solution looks like a straight string or a pair of straight and circular strings. The existence of such non-linear superposition of two strings becomes possible due to self-interaction terms in the Yang-Mills action which suppress contribution of the circular string near the polar axis.Comment: 21 pages, 11 figure

Microscopic derivation of Frenkel excitons in second quantization

Starting from the microscopic hamiltonian describing free electrons in a periodic lattice, we derive the hamiltonian appropriate to Frenkel excitons. This is done through a grouping of terms different from the one leading to Wannier excitons. This grouping makes appearing the atomic states as a relevant basis to describe Frenkel excitons in the second quantization. Using them, we derive the Frenkel exciton creation operators as well as the commutators which rule these operators and which make the Frenkel excitons differing from elementary bosons. The main goal of the present paper is to provide the necessary grounds for future works on Frenkel exciton many-body effects, with the composite nature of these particles treated exactly through a procedure similar to the one we have recently developed for Wannier excitons.Comment: 16 pages, 4 figure

A Note on Stress-Energy Tensor and Variational Principle for Null Strings

A straightforward application of the variational principle to null strings meets difficulties since string's world-sheets are degenerate. It is known that the variational principle in this case can be formulted with the help of two-vector density on the string world-sheet which plays a role of Lagrange multipliers. It is shown that recently suggested stress-energy tensor of null strings can be derived by variation over the background metric of the action used to describe tensionless limit in the string theory. One of the Lagrange multipliers is related to the energy of the null string.Comment: 4 page

Theory of a Narrow roton Absorption Line in the Spectrum of a Disk-Shaped SHF Resonator

We calculate the probability of the birth of a circular phonon (c-phonon) in He II by a c-photon of the resonator. It is shown that this probability has sharp maxima at frequencies, where the effective group velocity of the c-phonon is equal to zero; the density of states of c-phonons strongly grows at such frequencies. For He II, these frequencies correspond to a roton and a maxon. From the probability of the c-roton birth, we calculate the roto line width which is found to approximately agree with the experimental one. We conclude that the roton line observed in the super-high-frequency (SHF) absorption spectrum of helium is related to the birth of c-rotons. A possible interpretation of the Stark effect observed for the roton line is also proposed.Comment: 13 pages, 1 figure, v2: journal variant, several minor correction