h-Deformation of GL(1∣1)

An h-deformation of a (graded) Hopf algebra of functions on supergroup GL(11) is introduced via a contraction of GL _q (11). The deformation parameter h is odd (Grassmann). A related differential calculus on h-superplane is presented.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

Three-dimensional representation of the double quantum algebrasu q(η(J)) and theq-deformation of the double complex ernst equation

A three-dimensional representation of the double quantum algebrasu _q((J)) is given. By the use of this representation and a Lax pair, we obtain a nonlinear Ernst equation system. By the harmonic function method, a solution of theq-deformed double complex Ernst equation is given.     

Fusion rules of U q(sl(2, ℂ)), q m = 1

The decomposition of multiple tensor products of finite-dimensional irreducible representations of U _q(sl(2, )), for q's which are roots of 1, is studied in detail.     

Two-Parameter Deformation of the Oscillator Algebra and (p,q)–Analog of Two-Dimensional Conformal Field Theory

Abstract

The two-parameter deformation of canonical commutation relations is discussed. The self-adjointness property of the (p, q)-deformed position Q and momentum P operators is investigated. The (p, q)-analog of two-dimensional conformal field theory based on the (p, q)-deformation of the su(1, 1) subalgebra of the Virasoro algebra is presented.     

On the integral construction of the universal R-matrix for quantum current superalgebraUq (oŝp(1,2))

We discuss the problems in the construction of the universal R-matrix for the the Drinfeld current realization of quantum affine superalgebrasUq (oŝp(1,2)), where we try to present the universal R-matrix for the corresponding “Drinfeld” comultiplication in the form of certain integrals over current operators with specially chosen contours. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. Author’s research is partially supported by the Summer Research Fellowship and the Taft Foundation at the University of Cincinnati.     

Representation of Spin Group Spin（p, q）

The representation η（P, q） of spin group Spin（p, q） in any dimensional space is given by induction, and the relation between two representations, which are obtained in two kinds of inductions from Spin（p, q） to Spin（p ＋ 1, q ＋ 1） are studied.     

Integrable operator representations of ℝ q 2 ,X q,γ andSL q (2, ℝ)

We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a q-deformation of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of automorphisms of certain non-commutative rings of quotients coming from complex powers of quantum group generators; this is applied to explicit calculation of singular vectors in Verma modules over . We finally give a definition of aq-connection with coefficients in a ring of skew polynomials and study the structure of quantum group modules twisted by aq-connection.Supported by the Japan Society for the Promotion of Science Post-Doctoral Fellowship for Foreign Researchers in Japan.     

Iterative Construction of U q (s ℓ(n+1)) Representations and Lax Matrix Factorisation

The iterative construction of a generic representation of g?(n + 1) or of the trigonomentric deformation of its enveloping algebra is conveniently formulated in terms of Lax matrices. The Lax matrix of the constructed representation factorises into parts determined by the Lax matrix of a generic representation of the algebra with reduced rank and others appearing in the factorised expression of the Lax matrix of the special Jordan–Schwinger representation.     

Baxterization of ther-matrix for the adjoint representation of U q [D(2, 1;α)]

The Baxterization procedure is applied to the Braid group representation arising from the adjoint representation of the quantum supergroup U _q [D(2, 1;)]. This yields a two-parameter family of solutions to the (parameter dependent) Yang-Baxter equation of interest in supersymmetric lattice models.     

Simulation of the (p,T) phase diagram of the temperature-driven metamagnet α-FeRh

We perform finite-pressure Monte Carlo simulations of an effective spin-analogous model with coupled magnetic and lattice degrees of freedom, which has previously been proposed in order to explain the anomalous temperature driven metamagnetic phase transition in α-FeRh. The results are in reasonable agreement with the experimental (p,?T) phase diagram. The critical behaviour of the system along the transition lines is analysed in detail.     

Realisations of quantum GL p,q(2) and Jordanian GLh,h′(2)

The quantum group GL _p,q(2) is known to be related to the Jordanian GL_h,h(2) via a contraction procedure. It can also be realised using the generators of the Hopf algebra G _r,s. We contract the G _r,s quantum group to obtain its Jordanian analogue G _m,k, which provides a realisation of GL_h,h(2) in a manner similar to the q-deformed case.     

Bayesian inference of the resonance content of p(γ,K+)Λ

A bayesian analysis of the world's p(γ,K^+)Λ data is presented. From the proposed selection of 11 resonances, we find that the following nucleon resonances have the highest probability of contributing to the reaction: S11(1535), S11(1650), F15(1680), P13(1720), D13(1900), P13(1900), P11(1900), and F15(2000). We adopt a Regge-plus-resonance framework featuring consistent couplings for nucleon resonances up to spin J=5/2. We evaluate all possible combinations of 11 candidate resonances. The best model is selected from the 2048 model variants by calculating the bayesian evidence values against the world's p(γ,K+)Λ data.     

Distributions of products of the quasifree knocking-out reaction (p,p′n) on halo nuclei in the intermediate-energy region

Expressions for the distribution functions of products of the reaction (p, p′n) of valence neutron knocking-out from halo nuclei were derived using space-time correlation functions. The possibility of using this reaction to study the neutron halo structure was analyzed.     

Trapezoidal (p,q)-Integral Inequalities Related to (η1,η2)-convex Functions with Applications

In this paper, the authors introduce the (p,q)-trapezoidal integral inequalities, which are the (p,q)-analogues of the recently introduced q-trapezoidal integral inequalities. We derive a new (p,q)-integral identity for twice (p,q)-differentiable function. Utilizing this as an auxiliary result, we establish several new (p,q)-trapezoidal type integral inequalities for the function whose absolute value of twice (p,q)-derivative is (η₁,η₂)-convex functions. Some special means of real numbers are also given. At the end, we give brief conclusion. It is expected that this method which is very useful, accurate, and versatile will open a new venue for the real-world phenomena of special relativity and quantum theory.

     

First measurement of the exclusive (p,e+e−) reaction

We present the first data on the exclusive (p,e⁺e⁻) reaction in a nucleus. Cross sections for populating the ground state and first excited state in the residual nucleus are presented for the reaction ¹¹B(p, e⁺e⁻)¹²C at 98 MeV. The e⁺e⁻ momentum vectors were measured with a high-resolution magnetic pair spectrometer. The distributions of the virtual photon invariant mass and of the direction of the electron in the virtual photon rest system are compared with a simple single-nucleon model. The (p,e⁺e⁻) cross sections are compared with corresponding data for the (p, γ) reaction obtained with the same apparatus. The (p,e⁺e⁻) cross sections show substantial enhancement over what is expected from the simple model.     

Invariant Mass Spectroscopy of 23O via the (p, p′) Reaction in Inverse Kinematics

The neutron-rich oxygen isotope ²³O has been investigated via proton inelastic scattering on a liquid hydrogen target at 63.5 MeV/nucleon. The invariant mass method in inverse kinematics was employed to reconstruct the energy spectrum. A sharp resonance state was observed at 42(5) keV above the neutron threshold. A comparison of the differential cross section leading to this state with a microscopic DWBA calculation allowed a J ^π assignment of 5/2⁺ for this state.     

Unitary representations of suq(2) on the plane for q ∈ R+ or generic q ∈ S1

Some time ago, Rideau and Winternitz introduced a realization of the quantum algebra su _q(2) on a real two-dimensional sphere, or a real plane, and constructed a basis for its representations in terms of q-special functions, which can be expressed in terms of q-Vilenkin functions. In their study, the values of q were implicitly restricted to q R⁺. In the present paper, we extend their work to the case of generic values of q S ¹ (i.e., q values different from a root of unity). In addition, we unitarize the representations for both types of q values, q R⁺ and generic q S ¹, by determining some appropriate scalar products.     

Electronic spectra of XeNe molecules in the range 77100-90100 cm-1 near Xe* (6p, 5d, 6p’, 7s, 7p, 6d) obtained by the (3 + 1) REMPI and (2 + 1) REMPI methods

The electronic spectra of XeNe molecules in the range of 77100-90100 cm^-1 are measured by the method of laser resonance multiphoton ionization in a supersonic jet. The photoionization spectra are obtained upon two- and three-photon excitations of molecules and their ionization by the next photon. In the range of 80300-90100 cm^-1 near Xe*(5d, 6p’, 6d, 7s, and 7p), the spectra are obtained for the first time. A whole number of vibrational systems are measured in this range. The majority of vibrational systems near Xe* (5d, 6d, 7p, and 7s) are located in the red range with respect to their dissociation limits. In the blue range with respect to the dissociation limits, continua corresponding to transitions of molecules from the ground state to repulsive potential curves of excited states are detected. For a number of excited states of XeNe molecules, the vibrational analysis is performed and molecular constants are estimated.