On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Quantum Systems with Hidden Symmetry. Interbasis Expansions

This monograph is the English version of the book "Quantum systems with hidden symmetry. Interbasis expansions" published in 2006 by the publishing house FIZMATLIT (Moscow) in Russian. When compiling this version of the book, typos and inaccuracies noted since the release of the Russian edition have been corrected

All-particle primary energy spectrum in the 3-200 PeV energy range

We present all-particle primary cosmic-ray energy spectrum in the 3-200 PeV energy range obtained by a multi-parametric event-by-event evaluation of the primary energy. The results are obtained on the basis of an expanded EAS data set detected at mountain level (700 g/cm^2) by the GAMMA experiment. The energy evaluation method has been developed using the EAS simulation with the SIBYLL interaction model taking into account the response of GAMMA detectors and reconstruction uncertainties of EAS parameters. Nearly unbiased (<5%) energy estimations regardless of a primary nuclear mass with an accuracy of about 15-10% in the 3-200 PeV energy range respectively are attained. An irregularity ('bump') in the spectrum is observed at primary energies of ~74 PeV. This bump exceeds a smooth power-law fit to the data by about 4 standard deviations. Not rejecting stochastic nature of the bump completely, we examined the systematic uncertainties of our methods and conclude that they cannot be responsible for the observed feature.Comment: Accepted by J.Phys.G: Nucl.Part.Phy

Quantum oscillator as 1D anyon

It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe

Second Hopf map and Yang-Coulomb system on 5d (pseudo)sphere

Using the second Hopf map, we perform the reduction of the eight-dimensional (pseudo)spherical (Higgs)oscillator to a five-dimensional system interacting with a Yang monopole. Then, using a standard trick, we obtain, from the latter system, the pseudospherical and spherical generalizations of the Yang-Coulomb system (the five dimensional analog of MICZ-Kepler system). We present the whole set of its constants of motions, including the hidden symmetry generators given by the analog of Runge-Lenz vector. In the same way, starting from the eight-dimensional anisotropic inharmonic Higgs oscillator, we construct the integrable (pseudo)spherical generalization of the Yang-Coulomb system with the Stark term.Comment: 10 pages, PACS: 03.65.-w, 02.30.Ik, 14.80.H

Winding effects on brane/anti-brane pairs

We study a brane/anti-brane configuration which is separated along a compact direction by constructing a tachyon effective action which takes into account transverse scalars. Such an action is relevant in the study of HQCD model of Sakai and Sugimoto of chiral symmetry breaking, where the size of the compact circle sets the confinement scale. Our approach is motivated by string theory orbifold constructions and gives a route to model inhomogeneous tachyon decay. We illustrate the techniques involved with a relatively simple example of a harmonic oscillator on a circle. We will then repeat the analysis for the Sakai-Sugimoto model and show that by integrating out the winding modes will provide us with a renormalized action with a lower energy than that of truncating to zero winding sector.Comment: 21 pages, 3 figures. v3: discussion and references added, published versio