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.     

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 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.     

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.     

On nuclear states of [`(K)] \bar K mesons

The search for nuclear states of $ \bar K $ \bar K mesons poses interesting problems for the nuclear and low energy hadron physics: the behavior of tightly bound nuclear systems with strongly correlated impurities, the new kind of binding mechanisms and the extension of effective low energy theories to the strange sector. These problems are briefly presented and a method of variational calculation of the binding energies is discussed.     

Explaining GRB in the light of energy deposition rate for v+ [`(n)] \bar \nu → e+ + e? in a compact star

We have studied the v+ $ \bar \nu $ \bar \nu → e ⁺ + e ⁻ energy deposition rate near a rotating compact star which is important for the study of gamma ray bursts (GRB). The General relativistic (GR) and rotational effects increase the efficiency of the process immensely. The rotational effect also brings about an asymmetry in the deposition rate of the star.     

Preparation of quantum states of two spin-12 particles in the form of the Schmidt decomposition

We consider a system of two spins that are coupled via an isotropic Heisenberg Hamiltonian. For the first time, a two-step method for the preparation of an arbitrary quantum state of two qubits in the form of the Schmidt decomposition is proposed. The simplified version of this method is applied to the physical system of an atom with a nuclear spin 1/2 and one valence electron. As an example, the preparation of two-spin quantum states in the ³¹P system is considered.     

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.     

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.     

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.     

QCD Calculation ofK0 - [`(K)]0K^0 - \bar K^0 mixing from three-point function sum rules

We calculate theB parameter for mixing in the framework of QCD sum rules for a three-point function involving pseudoscalar currents, and contrast our results with other calculations. We findB=0.5±0.1±0.2, where the first error reflects uncertainties in the various QCD parameters and the second one is an estimate of uncalculated three-loop radiative and higher order quark mass corrections.     

Azimuthal peculiarities of gamma-ray-hadron families and the new physics at ?s\sqrt s ? TeVTeV

Summary Results of the analysis of possible causes of the alignment of energetically distinguished cores of γ-hadron families are presented. It is shown that the well-known physical factors cannot produce the observed effects. A phenomenological model based on new Pomeron physics theories and capable of explanation of this phenomenon is proposed. Paper presented at the Special Session on very high-energy cosmic-ray interactions (superfamilies) of the XXIV International Cosmic-Ray Conference, Rome, August 28–September 8, 1995.     

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.     

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.     

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.