On the schwarz problem for the [^(\textsu)]\text2 \widehat{{\text{su}}}_{\text{2}} Knizhnik-Zamolodchikov equation

We study the monodromy representations ^k,Iof the mapping class group ₄ acting on 4-point blocks satisfying the Knizhnik-Zamolodchikov equation for the levelk su₂ current algebra. We classify all irreducible ^k,Iwhich are realized by finite groups; we also display finite irreducible components for the reducible representations corresponding tok = 10.Supported by the Federal Ministry of Science and Research, Austria.     

PT\mathcal {P}\mathcal {T}-Symmetric Klein-Gordon Oscillator

Parity-time (PT)(\mathcal {P}\mathcal {T}) symmetric Klein-Gordon oscillator is presented using PT\mathcal {P}\mathcal {T}-symmetric minimal substitution. It is shown that wave equation is exactly solvable, and energy spectrum is the same as that of Hermitian Klein-Gordon oscillator presented by Bruce and Minning. Landau problem of PT\mathcal {P}\mathcal {T}-symmetric Klein-Gordon oscillator is discussed.     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

The property of maximal transcendentality in the N \mathcal{N} = 4 SYM

We show results for the universal anomalous dimension γ_uni(j) of Wilson twist-2 operators in the $ \mathcal{N} $ \mathcal{N} = 4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.     

The First Quantization of Spin \frac32\frac{3}{2} Field in de Sitter Space

The de Sitter solution to the positive cosmological Einstein field equation has been viewed as a one-sheeted hyperboloid embedded in a five dimensional Minkowski space. To find Lagrangian equation of supersymmetry-group in the de Sitter space, the different spinor field’s quantization have been demonstrated. In this work, the first quantization of spin field in the time-space de Sitter universe with ambient space notation has been done.     

Nuclear modification at ?{sNN }\sqrt {s_{NN} } = 17.3 GeV, measured at NA49

Transverse momentum spectra up to 4.5GeV/c were measured around midrapidity in Pb+Pb reactions at ?{s_NN }\sqrt {s_{NN} } = 17.3GeV, for π ^±, p, [`(p)]\bar p and K ^±, by the NA49 experiment. The nuclear modification factors R _AA , R _AA/pA and R _CP were extracted and are compared to RHIC results at ?{S_NN }\sqrt {S_{NN} } = 200GeV. The modification factor R _AA shows a rapid increase with transverse momentum in the covered region. The modification factor R _CP shows saturation well below unity in the π ^± channel. The extracted R _CP values follow the 200GeV RHIC results closely in the available transverse momentum range for all particle species. For π ^± above 2.5GeV/c transverse momentum, the measured suppression is smaller than that observed at RHIC. The nuclear modification factor R _AA/pA for π ^± stays well below unity.     

Free field realization of the level-2 elliptic algebra Ux,p ([^(\mathfraks\mathfrakl)]2 )*)U_{x,p} (\widehat{\mathfrak{s}\mathfrak{l}}_2 )*)

We give a level-2 representation of the elliptic algebra in terms of one free boson and one free fermion. We show that -modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the coset . Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Compactons in PT \mathcal{P}\mathcal{T} -symmetric generalized Korteweg-de Vries equations

This paper considers the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric equations a general theorem relating the energy, momentum and velocity of any solitarywave solution of the generalized KdV equation is derived. We also discuss the stability of the compacton solution as a function of the parameters affecting the nonlinearities.     

Description of Heavy Quark [`(MS)]\overline{MS} Mass by Lippmann-Schwinger Equation

Quark masses are of great prominence in high-energy physics. In this paper, we have studied the heavy meson systems via solving the Lippmann-Schwinger equation by using the Martin potential for heavy quark masses. We have also attempted to use Martin potential to find an acceptable mass spectrum for heavy quarkonia. We obtained this spectrum via minimal phenomenological model (Melles in Phys. Rev. D. 62:074019, 2000).     

Parabolic Presentations of the Super Yangian Y(\mathfrakglM|N){Y(\mathfrak{gl}_{M|N})}

Associated to a composition of M and a composition of N, a new presentation of the super Yangian of the general linear Lie superalgebra Y(\mathfrakgl_M|N){Y(\mathfrak{gl}_{M|N})} is obtained.     

PT\mathcal{PT}-Symmetry in (Generalized) Effect Algebras

We show that an η ₊-pseudo-Hermitian operator for some metric operator η ₊ of a quantum system described by a Hilbert space H{\mathcal{H}} yields an isomorphism between the partially ordered commutative group of linear maps on H{\mathcal{H}} and the partially ordered commutative group of linear maps on H_r+{\mathcal{H}}_{\rho_{+}}. The same applies to the generalized effect algebras of positive operators and to the effect algebras of c-bounded positive operators on the respective Hilbert spaces H{\mathcal{H}} and H_r+{\mathcal{H}}_{\rho_{+}}. Hence, from the standpoint of (generalized) effect algebra theory both representations of our quantum system coincide.     

PHENIX study of dihadron Δη correlation in Au + Au collision at ?{sNN } \sqrt {s_{NN} } = 200 GeV: the ridge

We show the recent study of the ridge phenomena by PHENIX Collaboration over a broad transverse momentum (p _T ) range. Properties of the ridge are extracted in terms of its shape in Δϕ and Δη, and its yield. These properties are found to be similar to the away-side modification in the same p _T range, suggesting a related modification mechanisms in both the near- and away-side.     

Yuri $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Ivanovich Tuzhilkin (on his 70th birthday)

Chronicle

Yuri $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Ivanovich Tuzhilkin (on his 70th birthday)     

A *-product on SL(2) and the corresponding nonstandard (\mathfrak{s}\mathfrak{l}({\text{2}}))

We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of dual to this, as well as a Poincaré basis for both algebras.Aspirant au Fonds National belge de la Recherche Scientifique. Partially supported by EEC contract SC1-0105-C.