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.     

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.     

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.     

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.     

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.     

Possible molecular states of D*s[`(D)]*sD^{*}_{s}\bar{D}^{*}_{s} system and Y(4140)

The interpretation of Y(4140) as a D^*_s[`(D)]<sup>*</sup><sub>s</sub>D^{*}_{s}\bar{D}^{*}_{s} molecule is studied dynamically in the one boson exchange approach, where σ, η and φ exchange are included. Ten allowed D<sup>*</sup><sub>s</sub>[`(D)]^*_sD^{*}_{s}\bar{D}^{*}_{s} states with low spin parity are considered, and we find that the J ^PC =0⁺⁺, 1⁺⁻, 0⁻⁺, 2⁺⁺ and 1⁻⁻ D^*_s[`(D)]<sup>*</sup><sub>s</sub>D^{*}_{s}\bar{D}^{*}_{s} configurations are most tightly bound. We suggest that the most favorable quantum numbers are J <sup>PC</sup> =0<sup>++</sup> for Y(4140) as a D<sup>*</sup><sub>s</sub>[`(D)]^*_sD^{*}_{s}\bar{D}^{*}_{s} molecule; however, J ^PC =0⁻⁺ and 2⁺⁺ cannot be excluded. We propose to search for the 1⁺⁻ and 1⁻⁻ partners in the J/ψ η and J/ψ η′ final states, which is an important test of the molecular hypothesis of Y(4140) and the reasonability of our model. The 0⁺⁺ B^*_s[`(B)]^*_sB^{*}_{s}\bar{B}^{*}_{s} molecule should be deeply bound; experimental search in the ϒ(1S)φ channel at Tevatron and LHC is suggested.     

A quantum dual pair \mathfraks\mathfrakl2 ,\mathfrakon \mathfrak{s}\mathfrak{l}_2 ,\mathfrak{o}_n and the associated Capelli identity

A quantum analogue of the dual pair is introduced in terms of the oscillator representation of U _q . Its commutant and the associated identity of Capelli type are discussed.     

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.     

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.     

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.     

Information on the Ostrovski $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Prize competition

Information

Information on the Ostrovski $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Prize competition     

K*0 and φ meson production in proton–nucleus interactions at ?s=41.6\textGeV\sqrt{s}=41.6\text{GeV}

The inclusive production cross sections of the strange vector mesons K^*0, K̄^*0, and φ have been measured in interactions of 920 GeV protons with C, Ti, and W targets with the HERA-B detector at the HERA storage ring. Differential cross sections as a function of rapidity and transverse momentum have been measured in the central rapidity region and for transverse momenta up to p_T = 3.5 GeV/c. The atomic number dependence is parametrised as σ_pA=σ_pN*A^α, where σ_pN is the proton–nucleon cross section. Within the phase space accessible, α(K^*0)=0.86±0.03, α(K̄^*0)=0.87±0.03, and α(φ)=0.96±0.02. The total proton–nucleon cross sections, determined by extrapolating the differential measurements to full phase space, are σ_pN→K*0=(5.06±0.54) mb, σ_pN→K̄*0=(4.02±0.45) mb, and σ_pN→φ=(1.17±0.11) mb. For all resonances the Cronin effect is observed; compared to the measurements of Cronin et al. for K^± mesons, the measured values of α for φ mesons coincide with those of K⁺ mesons for all transverse momenta, while the enhancement for K^*0/K̄^*0 mesons is smaller.     

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.     

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)     

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.     

Parabolic Presentations of the Super Yangian {Y(\mathfrak{gl}_{M|N})} Associated with Arbitrary 01-Sequences

Let μ be an arbitrary composition of M + N and let \({\mathfrak{s}}\) be an arbitrary \({0^{M}1^{N}}\)- sequence. A new presentation, depending on \({\mu \rm and \mathfrak{s}}\), of the super Yangian Y_M|N associated to the general linear Lie superalgebra \({\mathfrak{gl}_{M|N}}\) is obtained.     

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).     

A theoretical study on electron transfer in low-energy collisions of a collinear meta-stable with a $ {\rm{Na}}_3^ - $ {\rm{Na}}_3^ - " border="0"> Na

Electron transfer in the collisions of a with a Na is theoretically studied. It is assumed that the target is collinear (D _h ) and that its electronic state is meta-stable triplet state. Adiabatic potential energy surfaces and non-adiabatic couplings of the system are calculated by using a semi-empirical diatomics-in-molecules (DIM) method. The positions of (avoided)-crossings of potential surfaces are investigated and the non-adiabatic couplings between two different electronic states are calculated. An avoided crossing is found in the region where the separation between the target and projectile is relatively large (10–15 bohr). A dynamical calculation demonstrates that this crossing causes charge transfer between the target and projectile. Another intersection at a smaller separation changes the targets spin state (from triplet state to singlet state or vice versa). The cross-sections for charge and spin transfer reaction are estimated at the collision energy of 6.8 keV. It is found that the charge transfer cross-section is extremely enhanced when the target cluster ion is in its meta-stable triplet state comared to the case where the cluster is the ground singlet state.