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.     

Curvature of multiply warped products

In this paper, we study Ricci-flat and Einstein–Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of space–times called as generalized Kasner space–times, we apply our results to this kind of space–times as well as other relativistic space–times, i.e., Reissner–Nordström, Kasner space–times, Bañados–Teitelboim–Zanelli and de Sitter black hole solutions.     

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.     

Operator products in 2-dimensional critical theories

A noteworthy feature of certain conformally invariant 2-dimensional theories, such as the Ising and 3-state Potts models at the critical point, is the existence of “degenerate primary fields” associated with nullvectors of the Virasoro algebra. Such fields are endowed with a remarkably simple multiplication table under the operator product expansion, known as the fusion rules. In addition, correlation functions made up of these fields satisfy a system of linear homogeneous partial differential equations. We show here that these two properties are intimately related: for any n-point function, the number of conformally invariant solutions to the system of equations equals the number of times that the identity operator appears in the fusion of all n fields in the correlator. This theorem permits the calculation of some apparently intractable correlation functions. Finally, we generalize these ideas to the Neveu-Schwarz sector of superconformal theories.     

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 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 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.     

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     

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.     

Multiple-order rogue wave solutions to a (2+1)-dimensional Boussinesq type equation

In this paper, based on the Hirota bilinear method and symbolic computation approach, multiple-order rogue waves of (2+1)-dimensional Boussinesq type equation are constructed. The reduced bilinear form of the equation is deduced by the transformation of variables. Three kinds of rogue wave solutions are derived by means of bilinear equation. The maximum and minimum values of the first-order rogue wave solution are given at a specific moment. Furthermore, the second-order and third-order rogue waves are explicitly derived. The dynamic characteristics of three kinds of rogue wave solutions are shown by three-dimensional plot.     

The D'Alembert type waves and the soliton molecules in a (2+1)-dimensional Kadomtsev-Petviashvili with its hierarchy equation

For a one (2+1)-dimensional combined Kadomtsev-Petviashvili with its hierarchy equation, the missing D'Alembert type solution is derived first through the traveling wave transformation which contains several special kink molecule structures. Further, after introducing the Bäcklund transformation and an auxiliary variable, the N-soliton solution which contains some soliton molecules for this equation, is presented through its Hirota bilinear form. The concrete molecules including line solitons, breathers and a lump as well as several interactions of their hybrid are shown with the aid of special conditions and parameters. All these dynamical features are demonstrated through the different figures.     

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.