Stochastic quantization of gauge theories

The equivalence between a scalar quantum field theory in D dimensions and its classical counterpart in D + 2 dimensions which is coupled to an external random source with Gaussian correlations was observed by previous authors. This stochastic quantization is extended to gauge theories. The proof exploits the supersymmetry formalism suggested by Parisi and Sourlas.     

The topology of homophase misorientation spaces

Homophase misorientation spaces are investigated with a focus on the effect of symmetry operations on their topology and their minimum embedding dimensions in Euclidean space. Whereas the topology of rotation space is well established and requires a minimum of five variables for a one-to-one and continuous mapping, the spaces of orientations and misorientations are quotient spaces of the rotation space and are obtained by applying various equivalence relations. The equivalence relations for orientation spaces only involve the rotational symmetries of the underlying crystals. These spaces are classified under the three-dimensional manifolds called the spherical 3-manifolds, which have a non-trivial fundamental group, are not simply connected spaces, and do not embed in three-dimensional Euclidean space. In the case of homophase misorientation spaces, however, in addition to rotational symmetry operations there is a further ‘grain exchange symmetry’, which is shown to simplify the topology considerably. In some important cases this symmetry also reduces the number of Euclidean dimensions required to embed these misorientation spaces. The homophase misorientation spaces for the dihedral point groups D ₂(222), D ₄(422) and D ₆(622), the tetrahedral point group T(23), and the octahedral group O(432) are all found to be embeddable in only three dimensions, two dimensions less than required for rotations. Hence, these misorientation systems can be represented using three variables in a one-to-one and continuous manner.     

The fragility and rigidity of cosmological theories

The concepts of fragility and rigidity in theories containing a minimally coupled, self-interacting scalar field are introduced and defined for an arbitrary space-time dimension,D, by using the field as the dynamical variable. It is proved that inflation is rigid and the case of an exponential self-interaction is studied. The fragility of higher-order, scalar-tensor and Kaluza-Klein gravity theories is investigated by using their conformal equivalence to general relativity plus a scalar field. Whilst most higher-order theories are rigid, the conditions for Kaluza-Klein theories to become fragile depend strongly onD.     

Pure type I supergravity and DE 10

We establish a dynamical equivalence between the bosonic part of pure type I supergravity in D = 10 and a D = 1 non-linear σ-model on the Kac–Moody coset space DE ₁₀/K(DE ₁₀) if both theories are suitably truncated. To this end we make use of a decomposition of DE ₁₀ under its regular SO(9,9) subgroup. Our analysis also deals partly with the fermionic fields of the supergravity theory and we define corresponding representations of the generalised spatial Lorentz group K(DE ₁₀).     

Space-Time Fluctuations Induced by D-Branes and Their Effects on Neutrino Oscillations

Neutrino oscillations are analyzed in the Ellis-Mavromatos-Nanopoulos-Volkov (ENMV) model, where the quantum gravitational fluctuations of the space-time background are described by virtual D branes. Such fluctuations may induce neutrino oscillations if a violation of the equivalence principle or a tiny violation of the Lorentz invariance is imposed. In this framework, the oscillation length of neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the energy which is the scale characterizing the topological fluctuations in the vacuum.     

LETTER: Neutrino Oscillations Induced by Gravitational Recoil Effects

Quantum gravitational fluctuations of the space-time background, described by virtual D branes, may induce the neutrino oscillations if a tiny violation of the Lorentz invariance (or a violation of the equivalence principle) is required. In this approach, the oscillation length of massless neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the mass scale characterizing the topological fluctuations in the vacuum. Such a functional dependence on the energy is the same obtained in the framework of loop quantum gravity.     

Stabilization mechanism of turbulent premixed flames in strongly swirled flows

The stabilization of turbulent premixed flames in strongly swirled flows undergoing vortex breakdown is studied in the case of the ALSTOM En-Vironmental (EV) double cone burner using a simple one-dimensional boundary layer type model and computational fluid dynamics, mainly at the level of large-eddy simulation. The analysis shows that, due to flame curvature effects, the flame speed on the combustor axis is 2 D _t/R _F lower than the turbulent burning rate, where D _t is a characteristic turbulent diffusion coefficient and R _F the flame radius of curvature. Flame propagation with negative speed observed in the experiments, i.e. the flame completely embedded in the central recirculation zone on the symmetry axis, is explained with the one-dimensional model as caused by the factor 2 D _t/R _F being larger than the characteristic turbulent burning rate. A peculiar sudden displacement of the flame anchoring location deep into the burner, which takes place experimentally at a critical value of the equivalence ratio, cannot however be explained with the present one-dimensional approach due to the modelling assumptions. The mathematical analysis is supported in this case with large-eddy simulation which can accurately reproduce the flame behaviour across the full operating range. It is finally shown that steady RANS methods cannot cope with the problem due to their inability to correctly predict the velocity flowfield in this burner.     

正则化方法同化多普勒天气雷达资料及对降雨预报的影响

基于三维变分同化(3DVAR)的思想,提出一种适用于多普勒天气雷达资料直接同化的正则化方法.从寻求Y^o=H(X)带有偏差δ的极小模解出发,引入正则化思想,并给出与3DVAR方案不同的新代价函数.针对2008年8月14日发生在北京地区的一次局地暴雨过程,设计了一组数值试验,并采用L曲线准则后验选取最优正则化参数.数值结果表明:正则化方法和3DVAR方案均能有效同化多普勒雷达资料,雷达径向速度的同化效果明显好于反射率因 关键词： 多普勒雷达资料 正则化 3DVAR 降雨预报     

Structure of Lanczos-Lovelock Lagrangians in critical dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D-dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general covariance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension D = 2m and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in D = 2m. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, = _j R^j{R \sqrt{-g} = \partial_j R^j} for a doublet of functions R ^j  = (R ⁰, R ¹) which depends only on the metric and its first derivatives. We explicitly construct families of such R ^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in D = 4. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.     

The hopf algebra of vector fields on complex quantum groups

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A _n , B _n , C _n , and D _n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.Humboldt Fellow.     

Scale transformations for renormalized field operators: Discussion of the soluble model

We discuss the operator formulation of the Zachariasen-Thirring model, describing the chain approximation to the propagator (the sum of three-particle massless bubbles) in massless λ⁴ theory. Such a model is formally scale-invariant and explicitly soluble. All intermediate steps of conventional renormalization procedure, regularization, introduction of appropriate counterterms, and cut-off free limit, are explicitly performed. In every step the scaling properties are discussed and respective dilatation currents are written down. After the proper choice of scale transformations for the renormalized field operator, we obtain the nonlocal dilatation current, defining the renormalized dilatation generator D_Λ^R(t). In the cut-off free limit Λ → ∞ the ET commutator of D_Λ^R(t) with renormalized field operators reproduces the Callan-Symanzik modification of “naive” canonical scale transformations. The renormalized scale transformations coincide in the cut-off free limit with renormalized dimensional transformations and define the exact symmetry of the renormalized theory.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Two-loop relevant parts ofD-dimensional massive scalar one-loop integrals

The calculation of two-loop Feynman integrals within the dimensional regularization scheme requires the knowledge of scalar one-loop integrals up to the linear term inD-4. We give the corresponding explicit expressions in terms of polylogarithms for the general one-, two-and three-point function and for a special case of the fourpoint function needed for vertex corrections. Our results are valid in all kinematical regions for real masses and momenta.     

Invariant noncanonical mappings of singular theories. II

In a paper of the same title published in Physical Revview Dit was shown that in singular theories (i.e. theories incorporating constraints) non-canonical infinitesimal mappings that map equivalence classes intact on each other lead to the divergence of a vector field associated with the mapping constant throughout the equivalence class. The infinitesimal mappings form the germ of the group of finite mappings of equivalence classes on each other that change the form of the symplectic tensor field. Any non-canonical coordinate system on phase space thus obtained defines a scalar density field that is constant over an equivalence class. The constant of the motion obtained earlier represents the infinitesimal deviation of this new field from unity.     

On the resolution of singularities of multiple Mellin–Barnes integrals

One of the two existing strategies of resolving singularities of multifold Mellin–Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.m     

[2.2]Paracyclophane: theoretical study of its lower excited states and of the zero-field splitting parameters D

The lower excited singlet and triplet states and the zero-field splitting parameters D of [2.2]paracyclophane are studied within a semiempirical π theory which takes into account overlap effects between the two benzene rings, transanular and through-bond interaction via the methylene bridges. Whereas the singlet energies depend strongly on the through-bond interaction and the mutual polarization of σ core and π system this is not the case for the energies and zero-field splitting parameters D of the two lowest triplet states. The deformations of the benzene rings in [2.2]paracyclophane lead only to a small decrease of the excitation energies of about 0·2 eV. The D parameter can be written as a sum D = D_A + D_B + D_AB with the intrasubunit contributions D_A and D_B of the conjugated subunits A and B of the phane and an intersubunit term D_AB . We demonstrate that the deformations reduce the intrasubunit terms D_A and D_B and that they are crucial for the decrease of the D values of [2.2]paracyclophane with respect to p-xylene. The difference between the D values of the first and second triplet states is governed by the intersubunit term D_AB which has a different sign in the two states. However, this difference does not depend markedly on the transanular interaction. A further reduction of D_A and D_B in the first triplet state only is caused by transanular interaction by means of symmetrical charge-transfer terms in the wavefunction.     

Self-diffusion in liquid metals

A survey is made of all published data on self-diffusion in liquid metals and an examination is carried out on the temperature-dependence of D for studies covering a wide range of temperatures. Log D versus 1/T and D versus T represent the best data equally well, while D versus T ^1/2 and D versus T ² do not. The proper functional form is taken to be D=CT experimentally, and a simple free diffusion theory is developed from the standpoint of vibrational atom motion. An equation having no adjustable parameters results (D=k ² ? _D T/hk), in which κ is the vibrational force constant. Values calculated for D at the melting point are in good agreement with experimental values for potassium, sodium, copper and silver, but are below the measured values for lead, indium, zinc and tin.     

Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁)], necessarily entails perfect correlation for the pair of observables (D ₁₂, D ₂₂) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D ₁₂, D ₂₂)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D _ij, i,j = 1 or 2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.     

Relativistic star solutions in higher-dimensional pseudospheroidal space-time

We obtain relativistic solutions of a class of compact stars in hydrostatic equilibrium in higher dimensions by assuming a pseudospheroidal geometry for the spacetime. The space-time geometry is assumed to be (D − 1) pseudospheroid immersed in a D-dimensional Euclidean space. The spheroidicity parameter (λ) plays an important role in determining the equation of state of the matter content and the maximum radius of such stars. It is found that the core density of compact objects is approximately proportional to the square of the space-time dimensions (D), i.e., core of the star is denser in higher dimensions than that in conventional four dimensions. The central density of a compact star is also found to depend on the parameter λ. One obtains a physically interesting solution satisfying the acoustic condition when λ lies in the range λ > (D + 1)/(D − 3) for the space-time dimensions ranging from D = 4 to 8 and (D + 1)/(D − 3) < λ < (D ² − 4D + 3)/(D ² − 8D − 1) for space-time dimensions ≥9. The non-negativity of the energy density (ρ) constrains the parameter with a lower limit (λ > 1). We note that in the case of a superdense compact object the number of space-time dimensions cannot be taken infinitely large, which is a different result from the braneworld model.