Oblique warped products

We define the oblique warped products and prove their existence. In addition to the Levi-Civita connection we use both the Schouten–Van Kampen and Vr?nceanu connections to study the foliation and curvatures of an oblique warped product. As an application to cosmology we introduce the oblique Robertson–Walker spacetime and give its basic properties.     

Conformal hyperbolicity of Lorentzian warped products

A space-timeM is said to be conformally hyperbolic if the intrinsic conformal Lorentz pseudodistanced _M is a true distance. In this paper we first derive criteria which insure the conformal hyperbolicity of certain space-times which are generalizations of the Robertson-Walker spaces. Thend _M is determined explicitly for Einstein-de Sitter space, and important cosmological model.Author partially supported by NSF Grant No. MCS 80-03573.     

On the marginally trapped surfaces in 4-dimensional space-times with finite type Gauss map

In this paper we have studied the possibility of the center-of-mass energy of two particles colliding near the horizon of a static charged black hole in string theory. Various cases corresponding to the electric charge and the angular momentum of the particles were considered. The studies were done for the general black hole as well as for the extreme black hole. There were two scenarios where the center-of-mass energy reach very large values if the appropriate properties of the particles are chosen.     

On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.     

On the 4D effective theory in warped compactifications with fluxes and branes

We present a systematic way to derive the four-dimensional effective theories for warped compactifications with fluxes and branes in the ten-dimensional type IIB supergravity. The ten-dimensional equations of motion are solved using the gradient expansion method and the effective four-dimensional equations of motions are derived by imposing the consistency condition that the total derivative terms with respect to the six-dimensional internal coordinates vanish when integrated over the internal manifold. By solving the effective four-dimensional equations, we can find the gravitational backreaction to the warped geometry due to the dynamics of moduli fields, branes and fluxes.     

On the Darboux transformation for 1+2-dimensional equations

The Darboux transformations in 1+2-dimensional space are constructed, with a discussion of their composition and permutability. The auto-Bäcklund property of the Darboux transformation for the N x N system and KP hierarchy is also proved.     

On gravity localization under Lorentz violation in warped scenario

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher-dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem.     

On the critical behavior of (2 + 1)-dimensional QED

It is shown the analysis [1] for QED in (2 + 1) dimensions with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. As it was demonstrated in [1], the range of the admissible values N, where the dynamical fermion mass exists, decreases strongly with the increasing of the gauge charge. So, in Landau gauge the dynamical chiral symmetry breaking appears forN < 3.78, that is very close to the results of the leading order and in Feynman gauge dynamical mass is completely absent.     

On how the (1+1)-dimensional Dirac equation arises in classical physics

We demonstrate how the (1+1)-dimensional Dirac equation can be derived from the equation for the probability distribution governing a stochastic process when particles are permitted to propagate both backwards and forwards in time. This derivation uses a real transfer matrix and does not require a formal analytic continuation from classical physics. The physical significance of the quantity we interpret as being the wave function is discussed.     

On a (3 + 1)-dimensional solution of the Landau-Lifshitz equation

We obtain a new nonstationary solution of the nonlinear Landau-Liftshitz equation in three spatial dimensions for easy-axis ferromagnets and antiferromagnets in an external magnetic field. The solution has discrete axial symmetry and depending on the values of the free parameters, it can have the form of a multidomain periodic exchange structure or a domain boundary separating two semi-infinite regions of space. The singular behavior of the solution near the symmetry axis is pointed out.V. V. Kuibyshev State University, Tomsk. Institute of Applied Mathematics, Far-Eastern Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 68–71, June, 1994.     

Causality in 1+1-dimensional Yukawa model-II

The limits g → large, M → large with (g ³/M) ?=? const. of the 1+1-dimensional Yukawa model are discussed. The conclusion of the results on bound states of the Yukawa model in this limit (obtained in arXiv:0908.4510v3 [hep-th]) is taken into account. It is found that model reduces to an effective non-local ? ³ theory in this limit. Causality violation also is observed in this limit.     

On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that in such a quantum field theory (i) a continuous symmetry of (pseudo)scalar field translations is spontaneously broken, (ii) Goldstone bosons appear as quanta of a free massless (pseudo)scalar field and (iii) there is a non-vanishing spontaneous {magnetization}. In spite of the existence of a spontaneous {magnetization} the main inequality between vacuum expectation values of certain operators which have been used for the derivation of the Mermin–Wagner–Hohenberg theorem (C. Itzykson and J.-M. Drouffe, {Statistical field theory}, Vol. I, 1989, pp. 219–224) is fulfilled. Received: 19 December 2001 / Revised version: 31 March 2002 / Published online: 14 June 2002     

On the thermoluminescence of textile fibres

U.V. excited thermoluminescence of ten textile fibres is investigated above liquid N₂ temperature. The results seem to indicate that the glow peak peculiarities are mainly due to structural defects or chemical impurities. The kinetic order of the process is always found to be 1.     

Unconventional pairing in three-dimensional topological insulators with a warped surface state

We study the effect of the Fermi surface anisotropy (hexagonal warping) on the superconducting pair potential, induced in a three-dimensional topological insulator (TI) by proximity with an s-wave superconductor (S) in presence of a magnetic moment of a nearby ferromagnetic insulator (FI). In the previous studies, similar problem was treated with a simplified Hamiltonian, describing an isotropic Dirac cone dispersion. This approximation is only valid near the Dirac point. However, in topological insulators, the chemical potential often lies well above this point, where the Dirac cone is strongly anisotropic and its constant energy contour has a snowflake shape. Taking into account this shape, we show that a very exotic pair potential is induced on the topological insulator surface. Based on the symmetry arguments we also discuss the possibility of a supercurrent flowing along the S/FI interface, when an S/FI hybrid structure is formed on the TI surface.     

Exact form factors in (1 + 1)-dimensional field theoretic models with soliton behaviour

A system of equations is derived which must be satisfied by multiparticle matrix elements of any local operator in field theories with soliton behaviour. Form factors of various operators of interest are calculated exactly by means of the known exact S-matrices in the sine-Gordon, massive Thirring, non-linear σ^?, and Gross-Neveu models. The finite sine-Gordon wave function renormalization constant is determined exactly.