Deuteron form factors and the tensor force

Results of a non-relativistic calculation of deuteron form factors are presented for separable potentials with and without tensor force. The tensor term in triplet state is added in such a way as to keep the values of deuteron binding energy,a _t andr _0t unaltered, so that the difference in the form factors can be regarded as the effect of tensor force only. The calculation has been performed for two different shapes of separable potentials and for three differentD-state probabilities to study their comparative effect.     

Some remarks on braided group reconstruction and braided doubles

The cross coproduct braided group AutC)B is obtained by Tannaka-Krein reconstruction from C ^B C for a braided group B in braided category C. We apply this construction to obtain partial solutions to two problems in braided group theory, namely the tensor problem and the braided double. We obtain AutC) Aut(C) Aut(C) Aut(C) and higher braided group spin chains. The example B(R) B(R) ... B(R) is described explicitly by R-matrix relations. We also obtain Aut(C) Aut(C)* as a dual quasitriangular codouble braided group by reconstruction from the dual category C° C. General braided double crossproducts B C are also considered.     

Selective Decoupling

Low-power broadband decoupling sequences WALTZ-16 and GARP-1 generate large far-from-resonance frequency modulations which preclude selectivity. The framework developed to construct these broadband sequences is modified to permit selective spin decoupling. Selective-decoupling sequences are created from shaped 90° pulses combined consecutively using WALTZ permutations and supercycle symmetry while shaped 180° pulses are combined in supercycle symmetry to make inversion-based decoupling sequences. Simulations and experiments compare the decoupling bandwidth, frequency selectivity, and quality of near-resonance decoupling for broadband and selective-decoupling sequences.     

One-Shot Decoupling

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. One-shot decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.     

Lovelock tensor as generalized Einstein tensor

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler–Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss–Bonnet gravity as an another version of string–inspired gravity. This work was partially supported by a grant from the MSRT/Iran.     

Robust tensor estimation in diffusion tensor imaging

The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.     

Quantum and braided group Riemannian geometry

We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a principal bundle frame resolution and a dual pair of canonical forms. The role of Levi-Civita connection is naturally generalised to connections with vanishing torsion and cotorsion, which we introduce. We then provide the corresponding quantum group and braided group formulations with the universal quantum differential calculus. We also give general constructions, for example, including quantum spheres and quantum planes.     

Decoupling by a projection

The asymptotic behaviour for μ→∞ of the family H+μP is investigated, where H is a semi-bounded but not bounded selfadjoint operator, P is an orthoprojection, H is local with respect to $\text{P}\text{?}\text{=1?P}$. A characterization of the Friedrichs extension of

by the strong resolvent convergence limit of the family H+μP (which exists) is given. Applications to differential operators and strengthening of the main result (as to convergence with respect to the trace norm for some power of the resolvent) are discussed. Also an application to certain two space scattering systems is given.     

Decoupling of supersymmetric particles

The possibility of a heavy supersymmetric spectrum at the Minimal Supersymmetric Standard Model is considered and the decoupling from the low energy electroweak scale is analyzed in detail. The formal proof of decoupling of supersymmetric particles from low energy physics is stated in terms of the effective action for the particles of the Standard Model that results by integrating out all the sparticles in the limit where their masses are larger than the electroweak scale. The computation of the effective action for the standard electroweak gauge bosons , Z and is performed by integrating out all the squarks, sleptons, charginos and neutralinos to one-loop. The Higgs sector is not considered in this paper. The large sparticle masses limit is also analyzed in detail. Explicit analytical formulae for the two-point functions of the electroweak gauge bosons to be valid in that limit are presented. Finally, the decoupling of sparticles in the S, T and U parameters is studied analitically. A discussion on how the decoupling takes place in terms of both the physical sparticle masses and the non-physical mass parameters as the -parameter and the soft-breaking parameters is included. Received: 27 March 1998 / Published online: 5 October 1998     

Relative tensor calculus and the tensor time derivative

A relative tensor calculus is formulated for expressing equations of mathematical physics. A tensor time derivative operator ▽ _b ^a is defined which operates on tensors λ^ia...ib. Equations are written in a rigid, flat, inertial or other coordinate system a, altered to relative tensor notation, and are thereby expressed in general flowing coordinate systems or materials b, c, d, .... Mirror tensor expressions for ▽ _b ^a λ^ic...id and ▽ _b ^a λ_ic...id exist in a relative geometry G if and only if a rigid coordinate system a exists in G, where ▽ _b ^a λ^ic = λ _,0c ^ic + λ^kev _ckc ^aic + λ _kc ^ic v _b ^ckc , ▽_jcλ^ic = λ _,jc ^ic + λ^kcΓ _{jc kc} ^ie , and v _b ^aic is the velocity of b relative to a with components in c. These operators are convenient in theoretical analyses and can be incorporated into machine programs for the numerical solution of physical problems.     

Decoupling in supersymmetric theories

We examine the decoupling of massive states in supergravity theories. Using superspace functional techniques to “integrate out” the massive modes we derive the effective low-energy lagrangian. The technique is extended to the case of large supersymmetry breaking and we show how the effective lagrangian correctly accounts for vacuum expectation values of massive fields. We discuss the structure of effective theories following from the superstring in which the effects of Kaluza-Klein modes and states massive after intermediate scale breaking are included. It is shown in the case of large intermediate scale breaking the theory should possess discrete symmetries to protect light states from large supersymmetry breaking and we list the conditions for viable models.     

Decoupling of the two-pomeranchon-cut

We prove the decoupling of the two-Pomeranchon-cut from two Pomeranchon-Regge poles at zero momentum transfer. This implies the vanishing of the Pomeranchon-Pomeranchon-Reggeon vertex at zero momentum transfer.     

B to light tensor meson form factors derived from light-cone sum rules

Using the recent results for the two-parton light-cone distribution amplitudes of the tensor meson, we calculate the form factors for the decays of B_u,d,s$B_{u,d,s}$ into the light JPC=²⁺⁺$J^{\mathit{PC}}=2^{++}$ tensor mesons via the vector/axial–vector/tensor current with the light-cone sum rules. We also obtain the q²$q^2$-dependence of the form factors.     

On braided poisson and quantum inhomogeneous groups

The well known incompatibility between inhomogeneous quantum groups and the standardq-deformation is shown to disappear (at least in certain cases) when admitting the quantum group to be braided. Braided quantumISO(p, N - p) containingSO _q (p, N - p) with |q|=1 are constructed forN=2p, 2p + 1, 2p + 2. Their Poisson analogues (obtained first) are presented as an introduction to the quantum case. Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June 1997.     

q-Lorentz group and braided coaddition onq-Minkowski space

We present a new version ofq-Minkowski space, which has both a coaddition law and anSL _q (2, ) decomposition. The additive structure forms a braided group rather than a quantum one. In the process, we obtain aq-Lorentz group which coacts covariantly on thisq-Minkowski space.     

Decoupling in theories with anomalies

We consider the appearance of infinities due to the triangle anomaly in the Weinberg model by introducing terms in the lagrangian which restore the Ward identities. It is then shown that these are not the same as the divergence which occur in the standard model if the quarks (which cancel the anomalies) are given a large mass. We have not succeeded in finding a model in which the infinities due to the anomalies are the leading effects of heavy fermions.