Area-preserving diffeomorphisms and supermembrane Lorentz invariance

The Lie algebra of area-preserving diffeomorphisms on closed membranes of arbitrary topology is investigated. On the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane Lorentz generators. We derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated bySU(N). One of the additional tensors can then be identified with the invariant symmetric three-index tensor ofSU(N), while the second has no obvious analog. We prove that the Lorentz generators are classically conserved in the light-cone gauge for arbitrary membrane topology, as a consequence of these tensor identities. This formulation allows a systematic study of the violations of Lorentz invariance in theSU(N) approximation.     

Theoretical study of deuteron polarization in γ+d → π0+d

The state of polarization of the recoil deuteron in γ+d → π⁰+d on unpolarized and target polarized deuterons is analyzed in detail. A new set of statistical tensors is introduced to describe non-oriented systems, such as the recoil deuteron in γ+d → π⁰+d, and their relationships to the vector and tensor polarization parameters are established. The new statistical tensors reduce, in the case of oriented systems, to Fano's statistical tensors. Numerical results are computed using two different deuteron models for polarized photon asymmetry, polarized target asymmetry and the vector and tensor polarizations of the recoil deuteron, and these are presented at various c.m. pion production angles at different energies in the region of the first π-N resonance. The study of these parameters is suggested as a promising source of information on isoscalar pion photoproduction amplitudes.     

Unitary group decomposition of hamiltonian operators. II. SU (4) irreducible tensors,norms and their energy variation and symmetry breaking

SU(6) ? SU(4) tensor decomposition of effective interactions in the 2s-1d shell has been carried out to examine the relative importance of the various irreducible tensors in many-particle spaces. For this purpose norms of the irreducible tensors are evaluated in many-particle spaces. Variation of the expectation value of the square of the irreducible tensor parts with excitation energy has also been examined using the polynomial expansion method. A new measure of symmetry breaking that is theoretically more sound is derived which includes in its definition partial width as well as internal width. This is used to study SU(4) symmetry mixing in nuclei.     

The Polarization Tensors of Z → 3γ and γγ → γγ via W-Loop in the Standard Model

The polarization tensors of Z → 3γ and γγ → γγ W-Boson loops are calculated in the standard model. The constrained equations for the tensors are deduced from the crossing symmetry and gauge invariance. These equations are numerically checked by the polarization tensor of γγ → γγ to the first three lowest orders in its low energy expansion.     

Universal Star Products

One defines the notion of universal deformation quantization: given any manifold M, any Poisson structure Λ on M and any torsionfree linear connection ? on M, a universal deformation quantization associates to this data a star product on (M, Λ) given by a series of bidifferential operators whose corresponding tensors are given by universal polynomial expressions in the Poisson tensor Λ, the curvature tensor R and their covariant iterated derivatives. Such universal deformation quantization exist. We study their unicity at order 3 in the deformation parameter, computing the appropriate universal Poissoncohomology.     

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.     

EPR and ENDOR study of porphyrins and their covalently linked dimers in the photoexcited triplet state

The triplet states of several substituted porphyrins (Tetraphenylporphyrin (H₂TPP), Zinc-Tetramethylporphyrin (ZnTMP), Octaethylporphyrin (H₂OEP) and the Dication of H₂TPP (H₄TPP²⁺)) and two covalently linked dimers with H₂TPP-subunits in disordered solid solution were studied by EPR and ENDOR at liquid helium temperature. The measurement yields theA _zz component of the hyperfine tensors of all α-protons in the reference frame of the zero field splitting tensor. Dipolar and isotropic contributions toA _zz are discussed and spin densities derived. The spin densities are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/S). One of the dimers shows indications of triplet energy transfer between the porphyrin subunits. The order of magnitude of the transfer rate is estimated to be 5 · 10⁵ s^?1.     

A YANG–MILLS ELECTRODYNAMICS THEORY ON THE HOLOMORPHIC TANGENT BUNDLE

Considering a complex Lagrange space ([24]), in this paper the complex electromagnetic tensor fields are defined as the sum between the differential of the complex Liouville 1-form and the symplectic 2-form of the space relative to the adapted frames of the Chern–Lagrange complex nonlinear connection. In particular, an electrodynamics theory on a complex Finsler space is obtained.

We show that our definition of the complex electrodynamics tensors has physical meaning and these tensors generate an adequate field theory which offers the opportunity of coupling with the gravitation. The generalized complex Maxwell equations are written.

A gauge field theory of electrodynamics on the holomorphic tangent bundle is put over T′M and the gauge invariance to phase transformations is studied. An extension of the Dirac Lagrangian on T′M coupled with the electrodynamics Lagrangian is studied and it offers the framework for a unified gauge theory of fields.     

Fast stray field computation on tensor grids

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N^4/3 for N computational cells used and with N^2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.     

Solid-state 17O NMR study of the electric-field-gradient and chemical shielding tensors in polycrystalline γ-glycine

We report the first experimental determination of the carboxylate oxygen electric-field-gradient (EFG) and chemical shielding (CS) tensors in polycrystalline γ-glycine. Analysis of magic-angle spinning (MAS) and stationary ¹⁷O NMR spectra of [¹⁷O]-γ-glycine obtained at 9.4, 14.1, 16.4, and 18.8 T yields the magnitudes of the ¹⁷O EFG and CS tensors and the relative orientations between the two tensors. Extensive quantum chemical calculations at both the restricted Hartree–Fock and density functional levels have been performed to present the absolute tensor orientations in term of the molecular frame. We have demonstrated that ¹⁷O NMR tensor information could be unambiguously derived by the multiple field analyses of stationary ¹⁷O NMR spectra.     

Second and fourth order stark shifts in the 6snd 1 D 2 barium rydberg series

Stark splittings of⁶ snd ¹ D ₂ Rydberg states were measured betweenn=10 and 24 by quantum beat spectroscopy at very low electric field strengths, allowing the determination of tensor polarizabilities and atn=14, 19, and 24 the determination of tensor hyperpolarizabilities. The irregular behaviour of the tensor polarizabilities was explained by Coulomb approximation calculations. The fourth order contributions to the Stark Hamiltonian were written as effective operators. Representation in spherical tensor form gives tensors of rank zero, two, and four. The associated scalar and tensor hyperpolarizabilities were derived. Using these formulae, theoretical values for the hyperpolarizabilities were calculated.     

Quantization on a two-dimensional phase space with a constant curvature tensor

Some properties of the star product of the Weyl type (i.e., associated with the Weyl ordering) are proved. Fedosov construction of the *-product on a two-dimensional phase space with a constant curvature tensor is presented. Eigenvalue equations for momentum p and position q on a two-dimensional phase space with constant curvature tensors are solved.     

Separable dynamical systems: Characterization of separability structures on Riemannian manifolds

This paper is a direct continuation of the short note [1] on separability structures on Riemannian manifolds. A separability structure on a V_n is characterized by the existence of r Killing vectors and n–r Killing 2-tensors whose properties are briefly collected in a theorem. A general discussion on the form of the metric tensor and the Killing tensors components is given.     

The structure of Heesch groups and its relation to material property tensors

The magnetic crystal point groups (Heesch groups) are classified according to their structure with respect to the three inversion operations: space, time, and total inversion. Accordingly the tensors are classified by the irreducible representations of the full inversion group. The groups and tensors are considered under the action of the elements A_i of the group of automorphisms of the full inversion group. The following correspondence theorem is proved: The matrix form of the tensor representation T of the group G coincides with the matrix form of the representation A_iT of the group A_iG. The theorem gives a clear explanation of the so-called “magic numbers” and provides a suitable short cut for the calculation and tabulation of material property tensors.     

The significance of quadrupole-electric coefficients for the optical properties of nonmagnetic crystals

The physical significance of the quadrupole-electric tensor for the optical properties of nonmagnetic crystals is discussed. Some general symmetry properties between the optical material tensors are derived. As an example it is shown that the quadrupole-electric tensor induces the ellipticity of light which is reflected from crystals of the non centrosymmetric cubic classes 23 and ¯43m.     

Bound State Solutions of the Dirac Equation for the Eckart Potential with Coulomb-Like Yukawa-Like Tensor Interactions

In this paper, we present the approximate bound state solutions of the Dirac equation within the framework of spin and pseudospin symmetries for Eckart potential for arbitrary κ—state using Nikiforov–Uvarov method. The tensor interactions of Coulomb-like and Yukawa-like form are considered and the effects of these tensors and the degeneracy removing role are discussed in detail. Numerical results and figures to show the effect of the tensor interactions are also reported.     

Unusual representations of local groups

By means of duality transformations we obtain representations of Yang-Mills groups which are neither tensors nor gauge fields, and fields which under general coordinate transformations are neither tensors nor tensor densities.     

Energy and momentum in chiral theories

We calculate the energy momentum tensor to orderE ⁴ in chiral perturbation theory. New terms not present in previous work enter the effective Lagrangian. We describe these and estimate the values of the new coupling constants, using the results of a disperisve analysis of the π andK energy momentum tensors and relying on tensor meson dominance for the spin two component. In addition, we compare our findings with the predictions of known scalar meson dominance models of the conformal anomaly.     

Topology of spin Hamiltonian and crystal field tensors for Mn2+ in ZnSeO4·6H2O crystal

The expansion of the {B ₂} and {B ₄} tensors of the spin Hamiltonian (SH) for Mn²⁺ (⁶S-state) is performed in terms of the irreducible tensor products {V _{L 1} ?V _{L 2}}₂ and {V _{L 1} ?V _{L 2}}₄ of the crystal field (CF) tensors {V _{L 1}} and {V _{L 2}}. The EPR spectra of Mn²⁺ in the ZnSeO₄·6H₂O crystal are studied and the SH tensors {B ₂} and {B ₄} are calculated. The tensors {V ₄?V ₄}₂ and {V ₄?V ₄}₄ are computed using the point-charge model (PCM) of the [Zn(H₂O)₆] complex with the C₂ symmetry and are compared with the SH tensors {B ₂} and {B ₄}, respectively. The correct signs of the elements and the pseudo-symmety axes of the tensors are obtained both for the {B ₂} tensor and {V ₄?V ₄}₂ and for the {B ₄} tensor and {V ₄?V ₄}₄. It is concluded that the irreducible tensor products {V ₄?V ₄}₂ and {V ₄?V ₄}₄ provide the predominant contribution respectively to the SH tensors {B ₂} and {B ₄} of Mn²⁺.     

Tensor methods for the exceptional group E6

We present a tensor formalism to describe irreducible representations of the exceptional group E₆. Irreducible tensors are characterized by covariant and contravariant indices associated with the irreducible representation 27, and a third (orthogonal-type) index associated with the 78; contractions of these indices with a set of invariant tensors are required to vanish for irreducibility. The formalism is applied to the reduction of Kronecker products of E₆ irreducible representations. As a further illustration of the method, we construct explicitly the Higgs potential for scalar fields in the E₆ representations 27, 78, 351, 351′.