A(2)2 parafermions: a new conformal field theory

A new parafermionic algebra associated with the homogeneous space A⁽²⁾₂/U(1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A⁽²⁾₂ parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy–momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W-algebra type primary field with spin two.     

Millimeter-wave spectrum of the C4v molecule IOF5: l-type doubling of the kl = −1 transitions in the v11(E) = 1 state spectrum

Measurements of the rotational spectrum of the C_4v molecule IOF₅ are reported for the excited vibrational state v₁₁(E) = 1 for the transitions J13 ← 12, 14 ← 13, 16 ← 15, and 17 ← 16 (55–72 GHz) including the observation of the kl = −1 (q⁻), l-doubling effect. Detailed assignments of the E-state spectrum are presented based on the overlapping quadrupole structure. These data are analyzed together with earlier results for the excited vibrational state v₆(B₁) = 1 to give information concerning the ν₆(B₁)-ν₁₁(E) Coriolis interaction and the (Δl, Δk) = (2, 2) (q⁺) and (2, −2) (q⁻)l-resonance interactions. It is found that q₁₁⁻ = −2.57(10) MHz, |q₁₁⁺| = 0.094(20) MHz, Δ = ν₆ − ν₁₁ = 45.2(7) cm⁻, ζ_11,11^z = +0.18(1) and |ζ_6,11^y| = 0.73(4).     

Third-order theory of the line intensities in the allowed and forbidden vibrational-rotational bands of C3v molecules

A third-order theory of the intensities of the allowed and “forbidden” (perturbation-allowed) transitions to the fundamental vibrational levels of C_3v semirigid molecules has been worked out by using the method of contact transformations applied to the electric dipole moment operator. Explicit expressions have been obtained for the linestrengths of the allowed (Δk = 0, ±1) as well as forbidden (Δk = ±2, ±3, ±4) transitions from the ground vibronic state to the fundamental vibrational levels of C_3v molecules. The treatment takes into account all the important Coriolis and anharmonic interactions in a C_3v molecule, including the effect of the “2, 2” and “2, −1” l-type interactions and the Δk = ±3 interactions on the intensities of the allowed and forbidden vibrational-rotational transitions. The expressions for the linestrengths of the allowed and forbidden transitions are given here in a form suitable to fit the experimental data on the intensities in the vibrational-rotational spectra of C_3v molecules.     

Dual properties of orthogonal polynomials of discrete variables associated with the quantum algebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">su</Emphasis>(2))

We show that for every set of discrete polynomials y _n (x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials z _k (ξ(t)) of degrees k = s-a and k = b-s-1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative families. This allows us to obtain new expressions for the Clerbsch-Gordan and Racah coefficients of the quantum algebra U _q (su(2)) in terms of various Hahn and Racah q-polynomials. Dedicated to the memory of our teacher and friend Arnold F. Nikiforov (18.11.1930–27.12.2005).     

Single-particle potential in a chiral approach to nuclear matter including short-range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al.Phys. Lett. B 474, 7 (2000)) by calculating the underlying (complex-valued) single-particle potential U(p, k _f) + iW(p, k _f). The potential for a nucleon at the bottom of the Fermi sea, U(0, k _f0) = - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi surface. Also, the imaginary single-particle potential, W(0, k _f0) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear-matter equation of state can be obtained if the short-range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1π-exchange). We also consider the equation of state of pure neutron matter ˉE_n(k _n) and the asymmetry energy A(k _f) in that approach. The downward bending of these quantities above nuclear-matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics. Received: 19 December 2002 / Accepted: 11 February 2003 / Published online: 15 April 2003     

Schur duality in the toroidal setting

The classical Frobenius-Schur duality gives a correspondence between finite dimensional representations of the symmetric and the linear groups. The goal of the present paper is to extend this construction to the quantum toroidal setup with only elementary (algebraic) methods. This work can be seen as a continuation of [J, D1 and C2] (see also [C-P and G-R-V]) where the cases of the quantum groups U _q (sl(n)), Y(sl(n)) (the Yangian) and U _q (sl(n)) are given. In the toroidal setting the two algebras involved are deformations of Cherednik's double affine Hecke algebra introduced in [C1] and of the quantum toroidal group as given in [G-K-V]. Indeed, one should keep in mind the geometrical construction in [G-R-V] and [G-K-V] in terms of equivariant K-theory of some flag manifolds. A similar K-theoretic construction of Cherednik's algebra has motivated the present work. At last, we would like to lay emphasis on the fact that, contrary to [J, D1 and C2], the representations involved in our duality are infinite dimensional. Of course, in the classical case, i.e.,q=1, a similar duality holds between the toroidal Lie algebra and the toroidal version of the symmetric group. The authors would like to thank V. Ginzburg for a useful remark on a preceding version of this paper. Communicated by M. Jimbo     

Interference of Electromagnetic and Weak Interactions at High Energies and Neutral-Current μe Universality

A review is given on three types of experiments which recently detected the interference of electromagnetic and weak interactions at high energies in the reactions eD₂ → eX (SLAC, 1979), e⁺e⁻ → μ⁺μ⁻ (PETRA/PEP, 1981–83) and μ±C→μ±X (BCDMS, 1982). Asymmetry formulae are explicitely derived using the quark-parton model and the SU(2) × U(1) standard theory. With particular emphasis on the deep inelastic muon scattering experiment, the corresponding experiments are described and their results summarized. Combined fits to the 1983 asymmetry and νe data verify completely the muon-electron universality of the weak neutral current interaction giving for the vector and axial-vector coupling constants v_e = 0.02 ± 0.06, a_e = −0.54 ± 0.03 (electrons) and v_μ = −0.05 ± 0.16, a_μ = −0.51 ± 0.05 (muons).     

On Gell-Mann's λ-matrices,d- andf-tensors,octets, and parametrizations ofS U (3)

The algebra ofS U (3) is developed on the basis of the matrices _i ofGell-Mann, and identities involving the tensorsd _{i j k} andf _{i j k} occurring in their multiplication law are derived. Octets and the tensor analysis of the adjoint groupS U (3)/Z(3) ofS U (3) are discussed. Various explicit parametrizations ofS U (3) are presented as generalizations of familiarS U (2) results.     

The phase statistics of a multichannel radar interferometer

Abstract

The analysis in this paper is concerned with the problem of determining the phase statistics of the output of a multichannel coherent radar interferometer. The 2N channels of the radar consist of the outputs from N pairs of antennae. Each antenna receives a random electromagnetic wave field which has circular normal first-order statistics with an arbitrary coherence function. Each antenna in each pair receives a wave at a different time, the time difference Δt between each antenna in each pair being the same for all pairs. The signals received by each pair are independent. The signals from each pair are combined to give G(t, Δt)=Σ_k=1 ^N S_k(t) S_k*(t+Δt) where, for example, the signals from each antenna in the kth pair are S_k(t) and S_k(t+Δt).

The probability density function of the modulus and phase of G(t, Δt) is worked out. The joint density is shown to be a type of generalized K distribution, and the phase distribution is shown to be a hypergeometric function. The results show that it is possible to measure the phase of the coherence function of an electromagnetic wave field scattered from a randomly moving extended object (such as the ocean surface) using such a multichannel radar. This phase is related to asymmetry of the Doppler power spectrum. Furthermore, if this asymmetry is a result of surface currents on the ocean interacting with the surface waves which cause the electromagnetic scattering, then the surface currents may be measured in some sense.     

Pure rotational spectrum of cyanopropyne in the v12 = 1 vibrational state

The micoowave and millimeter-wave spectrum of cyanopropyne, CH₃CCCN, in the lowest excited vibrational state, v₁₂ = 1 (E), has been observed in the frequency range from 8 to 220 GHz. The measurements up to the J = 53−52 transitions allowed us to determine the Coriolis coupling term and the l-type interaction term very precisely in addition to some of the sextic centrifugal terms. The contribution of the r-type interaction (Δk = ±1, Δl = ±2) has been found to be correlated with that of η_J, a centrifugal correction term to the first-order Coriolis interaction.     

<Emphasis Type="Italic">O</Emphasis>(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits withO(12) algebra which breakF spin but preserves theF _z quantum numberM _F. The generators ofO(12) are derived and the quantum numberU ofO(12) for a given boson numberN is determined by identifying the corresponding quasi-spin algebra. TheO(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With theO(12) algebra identified, complete classification of pnIBM symmetry limits with goodM _F is established.     

Magnetic circularly polarized emission and magnetic circular dichroism of resolved vibronic lines in Cs2GeF6: Mn4+

Magnetic circularly polarized emission (M.C.P.E.) and magnetic circular dichroism (M.C.D.) techniques have been used to study at low temperatures resolved vibronic lines of the ⁴ A _2g ?² E_g transition in octahedral Mn⁴⁺(3d³) in the cubic host Cs₂GeF₆. Measurements have been made with applied magnetic field (and light propagation) along the [001] (F-Mn-F bond) and [111] directions. Though the Zeeman energy patterns are isotropic, the intensity patterns are not, and U′(Γ₈) eigenvectors for arbitrary field orientation have been derived. These have been used to calculate Zeeman intensity patterns for the [001] and [111] crystallographic directions, and the observed intensity variations with orientation are found to provide useful information about intensity mechanisms. In the case of the magnetic dipole origin, the intensity patterns as a function of orientation can be well accounted for by a first-order mechanism which, however, does not predict the small positive M.C.D. observed at the zero-field energy in the [111] orientation. A detailed analysis of this feature and previously measured energy spacings suggest that ζ_3d(Mn⁴⁺) should have a value of ～360 cm^-1 rather than the value 240 cm^-1 usually assumed. Electric dipole vibronic sidebands have been observed corresponding to v ₆(t _2u ), v ₄(t _1u ), v ₃(t _1u ), v ₄(t _1u ) + v ₅(t _2g ) and v ₂(e_g ) + v ₆(t _2u ). Using a U′→U′ vibronic intensity mechanism with spin-orbit mixing (Appendix A), the M.C.P.E. and total emission patterns for the first two of these regions can be quite well accounted for quantitatively. The corresponding M.C.D. in both cases, while in qualitative agreement with the M.C.P.E., shows much more complicated splitting patterns which are not explicable in terms of a simple k = 0 model. The other three vibronic regions can be accounted for qualitatively. In Appendix B a formula is derived which explicitly relates the M.C.P.E. of a vibronic emission line to its M.C.D. absorption counterpart.     

Space charge regions at silver halide surfaces: Experimental results for undoped AgCl

Vibrating capacitor measurements have been made of the variation with temperature of the surface potential of AgCl single crystals of surface orientation (100), (210), (110) and (111). The magnitude and temperature variation of the surface potential was found to be strongly dependent on the orientation of the free surface. The data are interpreted in terms of a model which attributes the existence of surface space charge potentials to differences in the binding energies of silver ions at surface sites relative to normal interior lattice sites. The results are summarized in terms of the Gibbs free energies ΔG_v^(hkl) for cation vacancy formation and give ΔG_v⁽¹¹⁰⁾ = + 0.01 eV + 5 kT, ΔG_v⁽¹⁰⁰⁾ = ? 0.2eV + 10 kT, ΔG_v⁽²¹⁰⁾ = = ? 0.8eV + 23kT, ΔG_v⁽¹¹¹⁾ = + 0.8 eV ? 20kT. These numbers have large absolute uncertainties but the relative values for the different orientations are reliable. The values of ΔG_v^hkl can be used to calculate the magnitude and sign of the surface space charge fields and allow some predictions on the formation of photographic latent images near free surfaces.     

Parafermionic theory with the symmetry Z5

A parafermionic conformal theory with the symmetry Z₅ is constructed, based on the second solution of Fateev–Zamolodchikov for the corresponding parafermionic chiral algebra.The primary operators of the theory, which are the singlet, doublet 1, doublet 2, and disorder operators, are found to be accommodated by the weight lattice of the classical Lie algebra B₂. The finite Kac tables for unitary theories are defined and the formula for the conformal dimensions of primary operators is given.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).     

量子混沌系统本征态的统计非遍历性及其半经典极限

讨论半经典极限下circular unitary ensemble(CUE)系综本征态θ_k(j)的非遍历性质.为研究量子系统本征态在统计上的非遍历性,定义了本征态分布ρ_k(j)的一对统计函数：Φ_N(j)=∑N-1k=0ρ_k(j)²和Ψ_N(j)=∑N-1k=0ρ_k(j),以分别体现量子本征态分布的凸起与凹陷.在随机矩阵理论的框架内,数值地计算了由正交归一的 关键词：     

Superconformal algebras and transitive group actions on quadrics

A classification of “physical” superconformal algebras is given. The list consists of seven algebras: the Virasoro algebra, the Neveu-Schwarz algebra, theN = 2,3 and 4 algebras, the superalgebra of all vector fields on theN = 2 supercircle, and a new algebraCK ₆ constructed in [3]. The proof relies heavily on the classification of all connected subgroups ofSO _n(C) which act transitively on the quadric (v, v) = 1. To Ernest Borisovich Vinberg on his 60_th birthday Partially supported by NSF grant DMS-9622870     

Dynamical Lie algebra method for highly excited vibrational state of asymmetric linear tetratomic molecules

The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric groupU ₁(4)U ₂(4)⊗U ₃(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M₁₂, M₁₃ and M₂₃, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C₂HF.     

(p,q)-Analog of Two-Dimensional Conformal Field Theory. The Ward Identities and Correlation Functions

Abstract

A (p, q)-analog of two-dimensional conformally invariant field theory based on the quantum algebra U_pq (su(1, 1)) is proposed. The representation of the algebra U_pq (su(1, 1)) on the space of quasi-primary fields is given. The (p, q)-deformed Ward identities of conformal field theory are defined. The two- and three-point correlation functions of quasi-primary fields are calculated.     

Discrete series of unitary irreducible representations of the Uq(u(3, 1)) and Uq(u(n, 1)) noncompact quantum algebras

The structure of all discrete series of unitary irreducible representations of the U _q (u(3, 1)) and U _q (u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′) _q . The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U _q (u(n, 1)) ⊇ U _q (u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra.