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1.
We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.  相似文献   

2.
Using the dimensional reduction characterizedM 6 =M 4×S2 as an example, it is demonstrated that higher-dimensional Einstein-Cartan (EC) gravity reduces to EC gravity with a cosmological term in four dimensions. A new higher-dimensional theory of gravity is proposed that results in EC gravitywithout cosmological term in four dimensions.  相似文献   

3.
To describe aromaticity of planar and three‐dimensional molecules, different electron counting rules are employed. Here, the relationship between the Hückel 4n + 2 rule and the Hirsch 2(n + 1)2 rule is established based on formal approach considering the electrons as objects in an arbitrary n‐dimensional space of states. Two types of three‐dimensional aromaticity, referred to as ‘spherical’ (following the 4n + 2 electron counting rule) and ‘spatial’ (following the 2(n + 1)2 electron counting rule) are distinguished. A conclusion concerning the boundaries of the Periodic Table of Elements is made based on the same formal approach that no g‐ (or higher) elements can exist and that possible extension of the Periodic Table beyond the seventh period must be followed by filling of the 8p or inner 6f or 7d levels. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

4.
Einstein equations are derived for D-dimensional space-time that spontaneously compactify to the product M4 × Πi = 1α Mdi in which the metric is taken to be of the generalized Robertson-Walker form. Cosmological solutions for these equations are studied with power law, oscillatory and exponential behaviour for the D-dimensional Einstein-Maxwell, N = 2, D = 10 and N = 1, D = 11 supergravity models. In the Einstein-Maxwell case the presence of a cosmological constant forces the extra dimensions to be static. Nevertheless, it is possible to find solutions with vanishing effective 4 dimensional cosmological constant with an expanding 4-dimensional space-time. In the supergravity models the requirement of having compact extra dimensions restricts the solutions to have expansion only in the 4-dimensional space-time. Matter contribution is added to the energy-momentum tensor in an attempt to find new solutions.  相似文献   

5.
The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s of the past century in a context of the HE Regge scattering. Recently, it has got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behaviour. We consider a QFT model gφ4 with running coupling defined in both domains of different dimensionality; the $ \bar g $ \bar g (q 2) evolutions being duly correlated at the reduction scale qM. Beyond this scale, in the deep UV 2-dimensional region, the running coupling does not increase any more. Instead, it slightly decreases and tends to a finite value $ \bar g $ \bar g 2(∞) < $ \bar g $ \bar g 2(M 2) from above. As a result, the global evolution picture looks quite peculiar and proposes a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.  相似文献   

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We construct a physical model to study the effects of dimensional reduction that might have taken place during the inflationary phase of the universe. The model we propose is a (1 + D)-dimensional (D > 3), nonsingular, spatially homogeneous and isotropic Friedmann model. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. Independent of the details of the process of dimensional reduction, we impose suitable boundary conditions across the transitions and trace the effects of dimensional reduction to the currently observable parameters of the universe. In order to exhibit the cosmological features of the proposed model, we construct a (1 + 4)-dimensional toy model for both closed and open cases of Friedmann geometries. It is shown that in these models the universe makes transition into the lower dimension when the critical length parameter l 4,3, which signals dimensional reduction, reaches the Planck length in D = 3. The numerical models we present in this paper have the capability of making definite predictions about the cosmological parameters of the universe such as the Hubble parameter, age and density.  相似文献   

9.
For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the -functions calculated using DRED transform into those computed in DREG. TheS-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.  相似文献   

10.
It has recently been suggested that our universe is a three-brane embedded in a higher dimensional spacetime. In this paper I examine static, spherically symmetric solutions that satisfy the effective Einstein field equations on a brane embedded in a five dimensional spacetime. The field equations involve a term depending on the five dimensional Weyl tensor, so that the solutions will not be Schwarzschild in general. This Weyl term is traceless so that any solution of (4) R = 0 is a possible four dimensional spacetime. Different solutions correspond to different five dimensional spacetimes and to different induced energy-momentum tensors on the brane. One interesting possibility is that the Weyl term could be responsible for the observed dark matter in the universe. It is shown that there are solutions of the equation (4) R = 0 that can account for the observed rotation curves of spiral galaxies.  相似文献   

11.
Two dimensional sine-Gordon (SG) field theory on a lattice is studied using the single-site basis variational method of Drell and others. The nature of the phase transition associated with the spontaneous symmetry breakdown in a SG field system is clarified to be of second order. A generalisation is offered for a SG-type field theory in two dimensions with a potential of the from [cos n (√λ/m)ϕ−1].  相似文献   

12.
Inhomogeneous multidimensional cosmological models with a higher-dimensional space-time manifold 0 i=1 n Mi (n 1) are in stigated under dimensional reduction to a D 0-dimensional effective non-minimally coupled -model which generalizes the familiar Brans–Dicke model. The general form of the Einstein frame representation of multidimensional solutions known in the Brans–Dicke frame is given with respect to cosmic synchronous time. As an example, the transformation is demonstrated explicitly for the generalized Kasner solutions where it is shown that solutions in the Einstein frame show no inflation of the external space although they can undergo deflation after the cosmic synchronous time inversion.  相似文献   

13.
Hot electron cooling rate P, due to acoustic phonons, is investigated in three‐dimensional Dirac fermion systems at low temperature taking account of the screening of electron–acoustic phonon interaction. P is studied as a function of electron temperature Te and electron concentration ne. Screening is found to suppress P very significantly for about Te < 0.5 K and its effect reduces considerably for about Te > 1 K in Cd3As2. In Bloch–Grüneisen (BG) regime, for screened (unscreened) case the Te dependence is PTe9(Te5) and the ne dependence gives Pne–5/3 (ne–1/3). The Te dependence is characteristic of 3D phonons and ne dependence is characteristics of 3D Dirac fermions. The plot of P /Te4 vs. Te shows a maximum at temperature Tem which shifts to higher values for larger ne. Interestingly, the maximum is nearly same for different ne and Tem/ne1/3 being nearly constant. More importantly, we propose, the ne dependent measurements of P would provide a clearer signature to identify 3D Dirac semimetal phase. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)  相似文献   

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The PF6?n(R)n? superhalogen anions (where R = CH3, C2H5 and n = 1–6) were investigated at the ab initio OVGF/6-311++G(3df,3pd)//MP2/6-311++G(d,p) level of theory and their electronic and thermodynamic stabilities were compared to those of the reference PF6? system. It is demonstrated that (1) the presence of six substituents bound to the phosphorus atom is an important factor that enables the stability of the PF6?n(R)n? anions; (2) subsequent replacement of the fluorine ligands with alkyl R groups in the PF6? superhalogen anion results in a substantial electronic stability decrease (by 2.38–6.74 eV); (3) when the certain number of alkyl substituents is achieved, the PF6?n(R)n? anions become thermodynamically unstable.  相似文献   

16.
We show that the weak-L 2 limit of a sequence of solutions of the two dimensional incompressible Euler equation is still a solution, provided that a (strong) concentration set for the reduced defect measure has locally finite one dimensional Hausdorff measure in space and time.  相似文献   

17.
By a direct calculation it is shown that at the three-loop level the regularization by dimensional reduction of Avdeev, Chochia and Vladimirov breaks supersymmetry relations between couplings in the N = 1, 2, 4 supersymmetric Yang-Mills theories written in terms of component fields. This is a strong limitation to the scope of the regularization.  相似文献   

18.
We study some properties of a class ofn-dimensional models which have infinite dimensional groups of symmetry which include both the Euclidean and Minkowskian groups. We show that all classical solutions of these models are self-dual and can be related to mappings of then dimensional hyper-space into itself which locally preserve the volume.  相似文献   

19.
LetS 1 andS 2 be independent simple random walks of lengthn inZ 4 starting at 0 andx 0 respectively. If |x 0|2n, it is shown that the probability that the paths intersect is of order (logn)–1. Ifx 0=0, it is shown that the probability of no intersection of the paths decays no faster than (logn)–1 and no slower than (logn)–1/2. It is conjectured that (logn)–1/2 is the actual decay rate.Research supported by National Science Foundation grant MCS-8002758  相似文献   

20.
The stability of anti-deSitter background solutions of gravity/scalar systems with respect to small fluetuations of the scalar fields is analyzed. As in the four dimensional case, one finds stability even about a local maximum provided that the effective scalar field masses are not “too tachyonic,” and for sufficiently low mass there are two possible boundary conditions that allow a well-defined and conserved energy. Unlike the d = 4 case only one boundary condition is applicable to the known gauged supergravity theories in d = 5 and d = 7. For d = 7 the stability criterion is satisfied while for d = 5 stability is marginal.  相似文献   

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