Kaluza-Klein towers in warped spaces with metric singularities

The version of the warp model that we proposed to explain the mass scale hierarchy has been extended by the introduction of one or more singularities in the metric. We restricted ourselves to a real massless scalar field supposed to propagate in a five dimensional bulk with the extradimension being compactified on a strip or on a circle. With the same emphasis on the hermiticity and commutativity properties of the Kakuza Klein operators, we have established all the allowed boundary conditions to be imposed on the fields. From them, for given positions of the singularities, one can deduce either mass eigenvalues building up a Kaluza Klein tower, or a tachyon, or a zero mass state. Assuming the Planck mass to be the high mass scale and by a choice, unique for all boundary conditions, of the major warp parameters, the low lying mass eigenvalues are of the order of the TeV, in this way explaining the mass scale hierarchy. In our model, the physical masses are related to the Kaluza Klein eigenvalues, depending on the location of the physical brane which is an arbitrary parameter of the model. Illustrative numerical calculations are given to visualize the structure of Kaluza Klein mass eigenvalue towers. Observation at high energy colliders like LHC of a mass tower with its characteristic structure would be the fingerprint of the model.Comment: 33 pages, 1 figur

Warped Kaluza-Klein Towers Revisited

Inspired by the warped Randall Sundrum scenario proposed to solve the mass scale hierarchy problem with a compactified fifth extra dimension, a similar model with no metric singularities has been elaborated. In this framework, the Kaluza-Klein reduction equations for a real massless scalar field propagating in the bulk have been studied carefully from the point of view of hermiticity so as to formulate in a mathematically rigorous way all the possible boundary conditions and corresponding mass eigenvalue towers and tachyon states. The physical masses as observable in our four-dimensional brane are deduced from these mass eigenvalues depending on the location of the brane on the extra dimension axis. Examples of mass towers and tachyons and related field probability densities are presented from numerical computations performed for some arbitrary choices of the parameters of the model.Comment: 34 pages, 5 figure

Elementary Kaluza-Klein Towers revisited

Considering that the momentum squared in the extra dimensions is the physically relevant quantity for the generation of the Kaluza-Klein mass states, we have reanalyzed mathematically the procedure for five dimensional scalar fields within the Arkhani-Ahmed, Dimopoulos and Dvali scenario. We find new sets of physically allowed boundary conditions. Beside the usual results, they lead to new towers with non regular mass spacing, to lonely mass states and to tachyons. We remark that, since the SO(1,4) symmetry is to be broken due to the compactification of the extra dimensions, the speed of light could be different in the fifth dimension. This would lead to the possible appearance of a new universal constant besides $\hbar$ and $c$.Comment: 20 pages, 1 figur

Kaluza-Klein towers for spinors in flat space

Considering a massive or massless free spinor field propagating in a flat five dimensional space with its fifth dimension compactified either on a strip or on a circle, we analyse the procedure of generation of the four dimensional Kaluza-Klein spinor mass towers. Requiring the five dimensional Dirac operator to be symmetric, the set of all the allowed boundary conditions is obtained. In the determination of the boundary conditions and in the Kaluza-Klein reduction equations, the SO(3,1) and parity invariances in the space-time subspace are carefully taken into account. The equations determining the mass towers are written in full generality. A few numerical examples are given.Comment: 17 page

Kaluza-Klein towers for spinors in warped spaces

All the boundary conditions compatible with the reduction of a five dimensional spinor field of bulk mass $M$ in a compactified warped space to a four dimensional brane are derived from the hermiticity conditions of the relevant operator. The possible presence of metric singularities is taken into account. Examples of resulting Kaluza-Klein spinor towers are given for a representative set of values for the basic parameters of the model and of the parameters describing the allowed boundary conditions, within the hypothesis that there exists one-mass-scale-only, the Planck mass. In many cases, the lowest mass in the tower is small and very sensitive to the parameters while the other masses are much higher and become more regularly spaced. In these cases, if a basic fermion of the standard model (lepton or quark) happens to be the lowest mass of a Kaluza-Klein tower, the other masses would be much larger and weakly dependent on the fermion which defines the tower.Comment: 39 page

Kaluza-Klein towers for real vector fields in flat space

We consider a free real vector field propagating in a five dimensional flat space with its fifth dimension compactified either on a strip or on a circle and perform a Kalaza Klein reduction which breaks SO(4,1) invariance while reserving SO(3,1) invariance. Taking into account the Lorenz gauge condition, we obtain from the most general hermiticity conditions for the relevant operators all the allowed boundary conditions which have to be imposed on the fields in the extra-dimension. The physical Kaluza-Klein mass towers, which result in a four-dimensional brane, are determined in the different distinct allowed cases. They depend on the bulk mass, on the parameters of the boundary conditions and on the extra parameter present in the Lagrangian. In general, they involve vector states together with accompanying scalar states.Comment: 28 pages, 4 independent table

保险代理手续费监管制度思考

本文应用博弈论的方法,基于保险代理手续费率市场化的发展趋势,分析了我国保险市场的发展现状与特点,回顾了我国保险代理手续费监管制度的发展过程和存在问题,指出目前在我国推行手续费率市场化的监管政策可能引发"手续费率资源化"问题,并就保险代理手续费市场化应建立在保险费率市场化方面提出政策建议

PROGRAMS FOR THE ANGULAR DISTRIBUTION ANALYSIS BY A MAXIMUM-LIKELIHOOD METHOD

Photograph of block print: "Fine Wind, Clear Morning" (Gaifū kaisei), also known as "South Wind, Clear Sky" or "Red Fuji", (from the series Thirty-six Views of Mt. Fuji), by Katsushika Hokusai (Japanese, 1760-1849), (approximate size, may vary slightly) 25.72 cm × 38 cm (10.125 in × 15 in), Edo period, circa 1831 - 1834"Fine Wind, Clear Morning" (Gaifu kaisei), also known as "South Wind, Clear Sky" or "Red Fuji", (from the series Thirty-six Views of Mt. Fuji), by Katsushika Hokusai (Japanese, 1760-1849), woodblock print, Edo period, circa 1831 - 1834

Interprétation théorique des constantes optiques dans les couches minces métalliques

Abstraet. — The optical constants of thin metallic films are interpreted in the case of gold and silver as being due to the progressive decrease, as thickness decreases, of the influence on the optical constants of a resonance (18 300 cm-1 and 22 500 cm-1 respectively). Palladium is characterized by the absence of a resonance in the interval investigated, extending from 18 300 cm-1 to 33 000 cm-1.Les constantes optiques des couches minces d'or et d'argent sont interprétées par une diminution progressive, lorsque l'épaisseur diminue, de l'influence sur les propriétés optiques d'une fréquence de résonance (18,300 cm -1 et 22,500 cm-1 respectivement). Les constantes optiques des couches minces de palladium se caractérisent par l'absence de fréquence de résonance dans l'intervalle spectral étudié s'étendant de 18,300 cm -1 à 33,000 cm-1