Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras

In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators . The reduction of the Poisson structure to the symplectic submanifold gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as , where means the multiplicity of roots and to the case (b) is defined by where is the multiplicity of poles. We prove that -algebra is isomorphic via a transformation to U(1) with m= . We also give the explicit free fields representations for these W-algebras.     

Projectively Equivariant Symbol Calculus

The spaces of linear differential operators acting on -densities on and the space of functions on which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (ⁿ) of vector fields of ⁿ. However, these modules are isomorphic as sl(n + 1,)-modules where is the Lie algebra of infinitesimal projective transformations. In addition, such an -equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the -equivariant symbol map to study the of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules .     

Integrals of Vertex Operators and uantum Shuffles

Given a braided vector space , we show that iterated integrals of operator-valued functions satisfying a certain exchange relation give rise to representations of the quantum shuffle algebra built on . Using the quantum shuffle construction of the 'upper triangular part' of a quantum shuffle, this provides a simple proof of the result of Bouwknegt, MacCarthy and Pilch saying that integrals of vertex operators acting on certain Fock modules give rise to representations of .     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

Bicross-Product Structure of Affine Quantum Groups

We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.     

BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings

Given a simple, simply laced, complex Lie algebra corresponding to the Lie group G, let be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra whose underlying graded commutative algebra is given by the cohomology, with respect to , of the algebra of regular functions on G with values in . We conjecture that describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical string. The conjecture is verified in the two explicitly known cases, ₂ (the Virasoro string) and ₃ (the string).     

Determination of heavy quark non-perturbative parametersfrom spectral moments in semileptonic B decays

Moments of the hadronic invariant mass and of the lepton energy spectra in semileptonic B decays have been determined with the data recorded by the DELPHI detector at LEP. From measurements of the inclusive b-hadron semileptonic decays, and imposing constraints from other measurements on b- and c-quark masses, the first three moments of the lepton energy distribution and of the hadronic mass distribution, have been used to determine parameters which enter into the extraction of |V_cb| from the measurement of the inclusive b-hadron semileptonic decay width. The values obtained in the kinetic scheme are: and include corrections at order 1/m_b³. Using these results, and present measurements of the inclusive semileptonic decay partial width of b-hadrons at LEP, an accurate determination of |V_cb| is obtained: Received: 26 April 2005, Revised: 16 September 2005, Published online: 16 November 2005     

Poincaré-Invariant Markov Processes and Gaussian Random Fields on Relativistic Phase Space

We give a complete characterization, including a Lévy–Itô decomposition, of Poincaré-invariant Markov processes on , the relativistic phase space in 1+1 spacetime dimensions. Then, by means of such processes, we construct Poincaré-invariant Gaussian random fields, and we prove a no-go theorem for the random fields corresponding to Brownian motions on .     

Multipoint Series of Gromov–Witten Invariants of CP1

We derive explicit formulas for the multipoint series of in degree 0 from the Toda hierarchy, using the recursions of the Toda hierarchy. The Toda equation then yields inductive formulas for the higher degree multipoint series of . We also obtain explicit formulas for the Hodge integrals , in the cases i=0 and 1.     

Generalized Cohomologies and the Physical Subspace of the SU(2) WZNW Model

The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that being the height of the current algebra representation) acts in -dimensional indefinite metric space of quantum group invariant vectors. The generalized cohomologies Ker are 1-dimensional. Their direct sum spans the physical subquotient of .     

Normal ordering and quantum groups

The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

Laplace Sequences of Surfaces in Projective Space and Two-Dimensional Toda Equations

We find that the Laplace sequences of surfaces of period n in projective space P _n–1 have two types, while type II occurs only for even n. The integrability condition of the fundamental equations of these two types have the same form

Search for double electron capture of 106Cd

A search for double electron capture of ¹⁰⁶Cd was performed at the Modane Underground Laboratory (4800 m w.e.) using a low-background and high-sensitivity multidetector spectrometer TGV-2 (Telescope Germanium Vertical). New limits on β ⁺/EC, EC/EC decays of ¹⁰⁶Cd were obtained from preliminary calculations of experimental data accumulated for 4800 h of measurement of 10 g of ¹⁰⁶Cd with enrichment of 75%. They are > 9.1 × 10¹⁸ yr, > 1.9 × 10¹⁹ yr for transitions to the first 2⁺, 511.9 keV excited state of ¹⁰⁶Pd, and > 1.3 × 10¹⁹ yr, > 6.2 × 10¹⁹ yr for transitions to the ground 0⁺ state of ¹⁰⁶Pd. All limits are given at 90% C.L. The text was submitted by the authors in English.     

Preferred Invariant Symplectic Connections on Compact Coadjoint Orbits

Let be the Haag--Kastler net generated by the (2) chiral current algebra at level 1. We classify the SL(2, )-covariant subsystems by showing that they are all fixed points nets ^H for some subgroup H of the gauge automorphisms group SO(3) of . Then, using the fact that the net ₁ generated by the (1) chiral current can be regarded as a subsystem of , we classify the subsystems of ₁. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem .     

Anomalies in the elastic properties of silicious iron single crystals at pressures of up to 9 GPa and the α−ɛ phase transformation

A Fe+5.07 at.%Si single crystal has been studied by ultrasonic-pulse technique. Its density and elastic constants were determined for p=0 and T=293 K. The dependence of the elastic properties of silicious iron on Si concentration was constructed. The compression, the effective elastic constants, and the Grüneisen parameters were measured at hydrostatic pressures of up to 9 GPa. It was found that for p=0, and . The elastic constants c ₄₄ and c′ increase linearly with pressure by 19.3 and 18.2% by p=9 GPa. The elastic anisotropy does not vary with pressure. For p>4 GPa, c ₁₁, c ₁₂, and K _S were observed to increase nonlinearly with decreasing pressure derivative. The Grüneisen parameter γ _LA decreases with pressure down to 0.70 at 9 GPa to become negative when extrapolated to the region of the α−ɛ phase transformation. The anomalies in c ₁₁ and the negative values of γ _LA for p>11 GPa indicate that the phase transformation in silicious iron at 13.5 GPa can take place by the crystallographic mechanism of the α−ɛ transformation in pure iron, i.e. by lattice compression in the [001] direction and shearing of the (110) planes along or . An assumption is put forward that pressure gives rise in silicious iron to sp-d hybridization, which results in increased screening of the ion-ion interaction and in anomalies in elastic properties. Similar phenomena are expected to occur in pure bcc Fe as well. Fiz. Tverd. Tela (St. Petersburg) 41, 516–522 (March 1999)     

A Generator for the Weert Superpotential

Weert found a superpotential for the bounded part of the Maxwelltensor associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator for the superpotential .     

A study of the nuclear-medium influence on neutral-strange-particle production in deep-inelastic neutrino scattering

The influence of nuclear effects on the production of neutral strange particles (V ⁰) is investigated using the data obtained with SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E _v =3−30 GeV) at the Serpukhov accelerator. The mean multiplicity of V ⁰ particles in nuclear interactions, , is found to exceed significantly that in “quasideuteron” interactions, . The ratio of is larger than that for π⁻ mesons, . It is shown that the multiplicity gain of V ⁰ particles can be explained by intranuclear interactions of produced pions. The text was submitted by the authors in English.     

Conformally Invariant Quantization at Order Three

Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.     

Al,F-doped new perovskite lithium fast ion conductor Li3x La2/3−x□1/3−2x Ti1−y Al y O3−y F y (x=0.11)

Al, F-doped new perovskite lithium ion conductors (x=0.11) have been prepared by solid state reaction. It is found that a pure perovskite-structured phase with space group of P4mm(99) exits in the composition range of 0<y≤0.10. The sample with y=0.02 possesses the highest ionic conductivity of 1.06×10⁻³ S/cm at room temperature, and its decomposing voltage is 2.3 V. The factors affecting the conductivity of this system are discussed.