Reconstruction of Five-Dimensional Bounce Cosmological Models from Deceleration Factor

In this paper, we consider a class of five-dimensional Ricci-flat vacuum solutions, which contain two arbitrary functions μ(t) and ν(t). It is shown that μ(t) can be rewritten as a new arbitrary function f(z) in terms of redshift z and the f(z) can be determined by choosing particular deceleration parameters q(z) which gives early deceleration and late time acceleration. In this way, the 5D cosmological model can be reconstructed and the evolution of the universe can be determined. PACS: 04.50.+h, 98.80.-k     

String cloud and domain walls with quark matter in 5-D Kaluza–Klein cosmological model

In this study Kaluza–Klein Cosmological solutions are obtained for quark matter coupled to the string cloud and domain wall in the context of general relativity. For this purpose Einstein field equations are solved by using anisotropy feature of the universe in the five-dimensional Kaluza–Klein Cosmological model. Also, the features of obtained solutions are discussed.     

A 5D noncompact and non Ricci flat Kaluza–Klein Cosmology

A model universe is proposed in the framework of 5D noncompact Kaluza–Klein cosmology which is not Ricci flat. The 4D part as the Robertson–Walker metric is coupled to conventional perfect fluid, and its extra-dimensional part is coupled to a dark pressure through a scalar field. It is shown that neither early inflation nor current acceleration of the 4D universe would happen if the nonvacuum states of the scalar field would contribute to 4D cosmology.     

The mechanism of generating fermion masses in the 8-dimensional geometric theory

The fermion sector of the 8-dimensional geometric Kaluza–Klein theory of gravi-strong interactions is considered. A mechanism of generating fermion masses via conformal (Weyl) transformations is proposed. It can be regarded as geometric analogue of the Higgs mechanism in standard gauge models. In this approach it is possible to eliminate Planck masses of particles which often appear in many Kaluza–Klein models of this type.     

Universal features of dimensional reduction schemes from general covariance breaking

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza–Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces, thus fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza–Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza–Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors.     

On the Klein–Gordon Equation in Higher Dimensions: Are Particle Masses Variable?

We consider ways to generalize the 4D Klein–Gordon equation of particle physics to higher dimensions. The most promising approach implies that the mass which appears in the 4D relation is a term in the source-free 5D relation. We check this explicitly for the case of exact solitonic and cosmological solutions of the Kaluza–Klein equations. In general, particle masses are variable; but are constant for the Schwarzschild and late-universe cases, in agreement with data from the solar system and astrophysics. Our results have significant implications for cosmology, and can easily be extended to 10D superstrings, 11D supergravity and higher dimensions.     

Effects of an additional dimension in the Young experiment

The results of the Young experiment can be analyzed either by classical or Quantum Physics. The later one though leads to a more complete interpretation, based on two different patterns that appear when one works either with single or double slits. Here we show that the two patterns can be derived from a single principle, in the context of General Relativity, if one assumes an additional spatial dimension to the four known today. The found equations yield the same results as those in Quantum Mechanics.     

Kaluza–Klein 5D Ideas Made Fully Geometric

After the 1916 success of general relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that under certain conditions like cylindricity (∂ g _ij /∂ x ⁵ = 0), the addition of the 5th dimension can explain the electromagnetic field. The problem with this approach is that while the model itself is geometric, conditions like cylindricity are not geometric. This problem was partly solved by Einstein and Bergman who proposed, in their 1938 paper, that the 5th dimension is compactified into a small circle S ¹ so that in the resulting cylindric 5D space-time R ⁴× S ¹ the dependence on x ⁵ is not macroscopically noticeable. We show that if, in all definitions of vectors, tensors, etc., we replace R ⁴ with R ⁴× S ¹, then conditions like cylindricity automatically follow – i.e., these conditions become fully geometric. PACS: 11.10.Kk Field theories in dimensions other than four, 04.50.+h Gravity in more than four dimensions.     

Letter: Generation of Solutions of the Einstein Equations by Means of the Kaluza–Klein Formulation

It is shown that starting from a solution of the Einstein–Maxwell equations coupled to a scalar field given by the Kaluza–Klein theory, invariant under a one-parameter group, one can obtain a one-parameter family of solutions of the same equations.     

The symmetries of the Manton superconductivity model

The symmetries and conserved quantities of Manton’s modified superconductivity model with non-relativistic Maxwell–Chern–Simons dynamics (also related to the Quantized Hall Effect) are obtained in the “Kaluza–Klein type” framework of Duval et al.     

Random-Cluster Representation of the Blume–Capel Model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∊ [1,2], and the ‘edge marginal’ when q ∊ [1,∞). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume–Capel model. Mathematics Subject Classification (2000): 82B20, 60K35.     

Solution to the Ghost Problem in Fourth Order Derivative Theories

We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais–Uhlenbeck fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais–Uhlenbeck model does indeed contain the negative norm energy eigenstates which are characteristic of higher derivative theories, in the limit in which we switch off the second order action, such ghost states are found to move off shell, with the spectrum of asymptotic in and out S-matrix states of the pure fourth order theory which results being found to be completely devoid of states with either negative energy or negative norm. We confirm these results by quantizing the Pais–Uhlenbeck theory via path integration and by constructing the associated first-quantized wave mechanics, and show that the disappearance of the would-be ghosts from the energy eigenspectrum in the pure fourth order limit is required by a hidden symmetry that the pure fourth order theory is unexpectedly found to possess. The occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure fourth order theories per se, but rather to be one which only arises when fourth and second order theories are coupled to each other.     

SU(2)Thirring模型边界算子的Boson表达式

得到了有边界的SU(2)Thirring模型的反射矩阵Rab(θ),以及相应的边界算子的Boson表达式.     

Exact Bosonic Solutions of the Truncated Skyrme Model

A model defined by half the Lagrangian （the highly nonlinear part） of the Skyrme model is investigated. Two classes of bosonic solutions are obtained. It is shown that, although the field configurations of these two classes are different, the energy densities for the two classes take the same form.     

A Gauge Theoretical View of the Charge Concept in Einstein Gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension /l ², the mass parameter of a particle dimension /l, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi–electric monopole charge of the time translation whereas the NUT parameter is a quasi–magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.     

Action Principle and Modification of the Faddeev–Popov Factor in Gauge Theories

The quantum action (dynamical) principle is exploited to investigate the nature and origin of the Faddeev–Popov (FP) factor in gauge theories without recourse to path integrals. Gauge invariant as well as gauge non-invariant interactions are considered to show that the FP factor needs to be modified in more general cases and expressions for these modifications are derived. In particular we show that a gauge invariant theory does not necessarily imply the familiar FP factor for proper quantization. PACS numbers: 11.15.-q; 12.10.-g; 12.15.-y; 12.38.-t     

The semileptonic form factors of B and D mesons in the Quark Confinement Model

The form factors of the weak currents, which appear in the semileptonic decays of the heavy pseudoscalar mesons are calculated within the quark confinement model by taking into account, for the first time, the structure of heavy-meson vertex and the finite quark mass contribution in the heavy-quark propagators. The results are in quite good agreement with the experimental data. Received: 9 June 2000 / Accepted: 15 August 2000     

Experimental details of the Stopped Beam RISING campaign

The RISING (Rare ISotope INvestigations at GSI) project constitutes a major pan-european initiative to study nuclear structure in exotic nuclei. A brief outline of the technical details specific to studies of isomeric decays following relativistic projectile fragmentation reactions is presented.     

Exact Solution for Jaynes-Cummings Model with Bosonic Field Nonlinearity and Strong Boson-Fermion Coupling

We use Lewis-Riesenfeld invariant approach to treat the modified Jaynes-Cummings models involving any forms of nonlinearty of the bosonic field when strong boson-fermion couplings are nilpotent Grassmann valued. The general state functions, time evolution operator and the time-evolution expressions for both the bosonic number and the fermionic number are presented.