First (fuzzy) Hopf map from irreps of SU(2)

Using the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S ³ we obtain spin-ν representation of the U(1) Hopf fibration S ³ → S ² as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles.     

Universality in the algebra of vertex strengths as generated by bilocal currents

We review the derivation of the algebra of vertex strengths (AVS) from the algebra of current bilocals on the null plane in the deep Regge scaling region (DRSR). We discuss the difficulties and present a mathematical procedure yielding AVS through a smooth removal of the divergent ω^α dependences which differ on both sides of the infinite “ω-local” algebra of scaling functions. We suggest that the S_a charges in AVS (the 2⁺⁺ trajectories' vertex strengths) may be given by the antisymmetrized matrix elements of the vector bilocals.     

Lax connections and solutions of the hybrid superstring on AdS 2 × S 2

In this paper, we show that the Lax connections can yield new classical solutions with a spectral parameter of the hybrid formulism for the Type IIB superstring in an AdS ₂ × S ² background with Ramond-Ramond flux. This series of classical solutions have the same infinite set of classically conserved charges.     

Macroscopic cell representation of density matrix equation and optimal choice of projectors by variational principle

We introduce a complete set of projectors on Liouvillespace and a “cell representation” of the equation of motion of the density matrixρ adjusted to the macroscopic observables of the system. Using a variational principle, the projector on the relevant density matrixρ _rel is determined by the postulate that the subdynamics ofρ _rel should include an optimal part of the Liouvillean?. The relation of the reduced subdynamics equation to wellknown master equations is investigated.     

Color dipole phenomenology of diffractive electroproduction of light vector mesons at HERA

We develop the color dipole phenomenology of diffractive photo- and electroproduction γ* N → V(V′)N of light vector mesons (V(1S) = ?⁰, ω⁰, ρ⁰) and their radial excitations (V′(2S) ?′, ω′, ρ′). The node of the radial wave function of the 2S states in conjunction with the energy dependence of the color dipole cross section is shown to lead to a strikingly different Q ² and ν dependence of diffractive production of the V(1S) and V′(2S) vector mesons. We discuss the restoration of flavor symmetry and universality properties of production of different vector mesons as a function of Q ² + m _V ² . The color dipole model predictions for the ρ ⁰ and ? ⁰ production are in good agreement with the experimental data from the EMC, NMC, ZEUS and H1 collaborations. We present the first direct evaluation of the dipole cross section from these data.     

Energy features of fissile nuclei at the scission point for various fission modes

Mass-spectroscopicdata on the yields of heavy products originating from the thermal-neutron-induced fission of ²³⁵U nuclei are presented over broad ranges of mass numbers A (125 ? A ? 155), kinetic energies E _k (40 ? E _k ? 80 MeV), and effective ion charges z* (18 ? z* ? 29). The potential energy of a fissile system at the scission point is analyzed with allowance for the positions of the minima that correspond to the most probable ways of separation of the system for the standard (S2) and superasymmetric (S3) fission modes.     

An effective lagrangian for multiphoton processes and a non-linear Born-Infeld lagrangian

An effective lagrangian for multiphoton processes (of Euler-Heisenberg type) is computed for an electromagnetic field interacting with massive scalar, fermion and vector particles. It is found that if the charges g_I, masses m_I and numbers N_I of massive particles satisfy the “supersymmetric” conditions, N_Sm_S⁴+3N_Vm_V⁴?2N_Fm_F⁴=0 and g_I²/m_I⁴ is I-independent, where I=S, F, V stands for scalars, fermions and vectors respectively, then not only quartic divergences (poles at n=0 in dimensional regularization) proportional to constant terms cancel out but also maximally helicity changing interaction terms vanish in the effective lagrangian. A possibility to relate a non-linear Born-Infeld lagrangian to the effective lagrangian is examined.     

S-wave state and D-wave state of the vector meson

The S-wave state ³ S ₁ and D-wave state ³ D ₁ are investigated by applying the Salpeter equation. The coupled equations of the S-wave component and the D-wave component are obtained. In nonrelativistic limit, the coupled equations are decoupled and reduced to two Schrödinger equations describing the S-wave state and the D-wave state, respectively. It is shown that the S-D coupling will be of order v ⁴ or of higher order. For vector mesons 1^??, the contribution to the decay constant comes only from the S-wave state in the nonrelativistic limit. Even when only the simple potential, the scalar and the zero component of the vector potential are considered and the orbit-spin term and tensor term are neglected, the D-wave contribution to the decay constant should also be considered in higher order.     

Force field of A(I)B(III)−S2 chalcopyrite compounds at zero wave vector

Published experimental frequencies are used to calculate Urey-Bradley force fields and ionic charges of some ABS₂ chalcopyrite compounds. The values obtained for the A?S and B?S force constants as well as the ionic charges are discussed.     

Residual Trace of Toeplitz or Pseudodifferential Projectors

The residual trace of a Toeplitz or pseudodifferential projector of degree 0 vanishes. This result is not necessarily true for projectors of degree \({\neq}\)0.     

J/ψ+η′ Production ine + e −-annihilation: A perturbative QCD calculation

The cross section for the reactione ⁺ e ^?→³S₁+¹S₀ is calculated in the framework of perturbative QCD, using the nonrelativistic approximation for the³S₁ and¹S₀ bound states. The model is applied toJ/Ψ plus η,η,η′, andl production. We find extremely small rates in contrast to previous estimates based on vector meson dominance and discuss possible reasons for this difference.     

Orientifolds and slumps in G2 and Spin(7) metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by , which are complete on a complex line bundle over . The principal orbits are S⁷, described as a triaxially squashed S³ bundle over S⁴. The behaviour in the S³ directions is similar to that in the Atiyah–Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S⁴. We then consider new G₂ metrics which we denote by , which are complete on an bundle over T^1,1, with principal orbits that are S³×S³. We study the metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S² cycles, and both carry magnetic charge with respect to the R–R vector field. We also discuss some four-dimensional hyper-Kähler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(∞) Toda equation, which can provide a way of studying their interior structure.     

Colored,spinning classical particle in an external non-abelian gauge field

We derive classical non-relativistic equations of motion for a colored, spinning point-like particle in an external SU(2) gauge field from Dirac equation. We find that in addition to the classical spin and color spin vector, S, I, it is necessary to introduce a new classical dynamical variable [J^ab], a, b = 1, 2, 3, describing a mixing of the spin and color. The constraint relations between [J^ab], S, I are also found.     

Structural,electronic and magnetic properties of the double perovskite Pb2FeReO6

The structural, electronic and magnetic properties of the double perovskite Pb₂FeReO₆ have been studied by using the first-principles projector augmented wave (PAW) potential within the generalized gradient approximation (GGA) as well as taking into account the on-site Coulomb repulsive and exchange coupling interactions (GGA+U). The optimized crystal structure of the Pb₂FeReO₆ is a body-centered tetragonal (BCT) with a space group of I4/m and the lattice constants of a=b=5.59 Å and c=7.93 Å, consistent with the experimental results. The two axial transition metal and oxygen (TM–O) distances are slightly larger than the four equatorial TM–O distances and shows the existence of the Jahn–Teller structural distortion in FeO₆ and ReO₆ octahedra. The Fe³⁺ and Re⁵⁺ ions are in the states (3d⁵, S=5/2) and (5d², S=1) with magnetic moments 3.929 and −0.831μ_B respectively and thus antiferromagnetic (AFM) coupling via oxygen between them. The half-metallic (HM) ferromagnetic (FM) nature implies a potential application of this new compound in magnetoelectronic and spintronics devices.     

Half-metallic ferromagnetic nature of the double perovskite Pb2FeMoO6 from first-principle calculations

The structural, electronic and magnetic properties of the double perovskite Pb₂FeMoO₆ have been studied by using the first-principle projector augmented wave (PAW) potential within the generalized gradient approximation (GGA) as well as taking into account the on-site Coulomb repulsive interaction (GGA+U). Similar to Sr₂FeMoO₆ and Pb₂FeReO₆, the optimized crystal structure of Pb₂FeMoO₆ is a body-centered tetragonal (BCT) with the lattice constants a=b=5.60 Å and c=7.94 Å. The two axial TM?O distances are slightly larger than the four equatorial TM?O distances, which shows that the Jahn–Teller structural distortion exists in FeO₆ and MoO₆ octahedra. The half-metallic ferromagnetic nature implies a potential application of this new compound in spintronics devices. The Fe³⁺ and Mo⁵⁺ ions are in the states (3d⁵, S=5/2) and (4d¹, S=1/2) with magnetic moments 3.87 and ?0.38μ_B respectively and thus there exists an antiferromagnetic coupling via oxygen between them.     

A compact rotating gravitational instanton

A compact rotating gravitational instanton (a positive-definite metric solution of the Einstein equations with Λ term) is presented. The manifold is the nontrivial S² fibre bundle over S² and has χ = 4, τ = 0, but no spinor structure. The metric can be obtained from a special limit of the positive-definite analytic extension of the Kerr-de Sitter metric or alternatively from the Taub-NUT metric with Λ term. The action is about $\text{4}\text{1}\text{2}\text{\%}$ less negative than that of the Einstein metric on the trivial bundle S² × S².     

Absence of particle production and factorization of the S-matrix in 1 + 1 dimensional models

In massive, 1 + 1 dimensional, local, quantum field theories the existence of two conserved charges is shown to be a sufficient condition for the absence of particle production and factorization of the S-matrix. These charges must commute and be integrals of local current densities. Their transformation properties under the Lorentz group must be different and also different from the transformation properties of a vector or a scalar. Also, they must not annihilate any single-particle momentum eigenstate.     

Local Index Formula on the Equatorial Podleś Sphere

We discuss spectral properties of the equatorial Podleś sphere S _q ². As a preparation we also study the ‘degenerate’ (i.e. q=0) case (related to the quantum disk). Over S _q ² we consider two different spectral triples:one related to the Fock representation of the Toeplitz algebra and the isopectral one given in [7]. After the identification of the smooth pre-C ^*-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the C ^*-algebra (the nontrivial generator of the K ₀-group) as well as the pairing with the q-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.     

Unbiased projector basis over C3

We discuss properties of an unbiased projector basis over C³. It is shown that such bases may be convenient for handling positive (nonnegative) operators, allowing, e.g., a state of a quantum system to be given as a set of four probability distributions.     

Angular distributions of penning electrons

Angular distributions of electrons ejected in thermal collisions of He(2¹ S, 2³ S)-metastables with Ar, Kr, Xe, Hg, CO, N₂ are measured with respect to the vector of relative velocity of the colliding particles. Except for preliminary results on the He(2₁S, 2³ S)-/Ar-system, these are the first such distributions reported. They are found to be strongly anisotropic and asymmetric in some cases, and approximately isotropic in those cases where the interaction potential between the metastable- and the target particle is strong. For the cases of weak interaction potential, the connection between the “internal” angular distribution in the frame fixed to the internuclear axis and the laboratory angular distribution, has been derived. Calculations of laboratory angular distributions involving an assumed “internal” distribution and the kinematics of a hard core collision show good qualitative agreement with the experimental results.