Theoretical prediction of cosmological constant Λ in Veneziano ghost theory of QCD

Based on the Veneziano ghost theory of QCD, we predict the cosmological constant ??, which is related to energy density of cosmological vacuum by $ \Lambda = \frac{{8\pi G}} {3}\rho _\Lambda $ . In the Veneziano ghost theory, the vacuum energy density ?? _?? is expressed by absolute value of the product of quark vacuum condensate and quark current mass: $ \rho _\Lambda = \frac{{2N_f H}} {{m_{\eta '} }}c|m_q < 0|:\bar qq:|0 > | $ . We calculate the quark local vacuum condensates ??0|: $ \bar q $ q: |0?? by solving Dyson-Schwinger Equations for a fully dressed confining quark propagator S _f (p) with an effective gluon propagator G _???? ^ab (q). The quark current mass m _q is predicted by use of chiral perturbation theory. Our theoretical result of ??, with the resulting ??0|: 471-4 q: |0?? = ?(235 MeV)³ and light quark current mass m _q ? 3.29?C6.15 MeV, is in a good agreement with the observable of the ?? ?? 10^?52 m^?2 used widely in a great amount of literatures.     

Differential calculus on the quantum superspace and deformation of phase space

We investigate non-commutative differential calculus on the supersymmetric version of quantum space in which quantum supergroups are realized. Multiparametric quantum deformation of the general linear super-group,GL _q(m|n), is studied and the explicit form for the \(\hat R - matrix\) is presented. We apply these results to the quantum phase-space construction ofOSp _q(2n|2m) and calculate their \(\hat R - matrices\) .     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Is there a 2++ glueball at 1410 MeV?

A glueball component of theJ ^PC =2⁺⁺ q \(\bar q\) isoscalar states is discussed within a simple mass mixing model. As the third isoscalar necessarily present in theq \(\bar q\) ?gg mixing scheme we assumeG(1410) recently claimed by ACCMOR Collaboration in the π^? p→K _s ⁰ K _s ⁰ n data. The hypothesis is found to be compatible with the available experimental data, including two-photon decay widths and radiativeJ/ψ decays.     

Form factor π0 → γ* + γ* at different photon virtualities

The π⁰ γγ vertex for virtual photons of squared masses q ₁ ² and q ₂ ² plays a vital rôle in several physical processes; for example for q ₁ ² < 0, q ₂ ² < 0, in the two-photon physics reaction e ⁺ e ^? → e ⁺ e ^?π⁰, and for q ₁ ² > 0, q ₂ ² > 0, in the annihilation process e ⁺ e ^? → π⁰ l ⁺l^?. It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expression for the vertex in the limit in which at least one of ¦q ₁ ² ¦ and ¦q ₂ ² ¦ is large for arbitrary fixed values of the ratio q ₁ ² /q ₂ ² . We compare our results with those obtained previously by Brodsky and Lepage. It should be straightforward to test our predictions experimentally.     

Ground-state energy of quantum liquids

The kinetic (K ₄ ⁰ (n) and K ₃ ⁰ (n)) and potential (V ₄ ⁰ (n) and V ₃ ⁰ (n)) energies of ⁴He and ³He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies E ₄ ⁰ (n) and E ₃ ⁰ (n) on the density of the isotopes ⁴He and ³He. In the approximation of structureless quantum liquid, the potential energies are equal, V ₄ ⁰ V ₃ ⁰ (n) = (n), and the kinetic energies are inversely proportional to the atomic mass, $K_4^0 (n) = \frac{3} {4}K_3^0 (n)$ . The potential energy given by the expression V ⁰ = 4E ₄ ⁰ ? 3E ₃ ⁰ to a high accuracy is linear in the density n, which is associated with nearly an absence of short-range order in liquid helium. The kinetic energy of liquid ⁴He is given by the expression K ₄ ⁰ = 3(E ₃ ⁰ ? E ₄ ⁰ ), which agrees with the experimental data on neutron scattering in liquid ⁴He. The quantities K ₄ ⁰ (n) and K ₃ ⁰ (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.     

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫ ₀ ^∞ r ^m 〈u(x)ω(x + r)〉 dr = I _m ^h (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from ?3/2 to ?5/2 versus the interval from ?6/5 to ?10/7 for the energy.     

Hyperfine structure of EPR spectra of Gd3+ odd isotopes in PbMoO4, Pb5Ge3O11, YVO4, and quadrupole interaction (temperature dependence)

A hyperfine structure of EPR signals of odd isotopes Gd³⁺ in Pb₅Ge₃O₁₁, PbMoO₄, and YVO₄ single crystals has been investigated at different temperatures. The observation of forbidden (with the nuclear spin flip) transitions has made it possible to determine quadrupole interaction P ₂ ⁰ associated with the gradient of the electric field of ligands at the impurity. It has been shown for the first time that, under the condition |P ₂ ⁰ | ≥ |A _{x, y} | (A _i are the tensor components), not only the magnitudes of splitting but also the observed asymmetry in a hyperfine structure (in perpendicular orientations of the magnetic field) depends on mutual signs of parameters of initial splitting b ₂ ⁰ and P ₂ ⁰ . Results of studying the spectra have demonstrated that |b ₂ ⁰ (T)|/|P ₂ ⁰ (T)| ～ const for a concrete single crystal, which assumes the similarity of physical mechanisms determining these parameters.     

Limit behavior of saturated approximations of nonlinear Schrödinger equation

We consider the solutionu _?(t) of the saturated nonlinear Schrödinger equation (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} u + \varepsilon \left| u \right|^{q - 1} uandu(0,.) = \varphi (.)$$ where \(N \geqslant 2,\varepsilon > 0,1 + 4/N< q< (N + 2)/(N - 2),u:\mathbb{R} \times \mathbb{R}^N \to \mathbb{C},\varphi \) , ? is a radially symmetric function inH ¹(R ^N ). We assume that the solution of the limit equation is not globally defined in time. There is aT>0 such that \(\mathop {\lim }\limits_{t \to T} \left\| {u(t)} \right\|_{H^1 } = + \infty \) , whereu(t) is solution of (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} uandu(0,.) = \varphi (.)$$ For ?>0 fixed,u _?(t) is defined for all time. We are interested in the limit behavior as ?→0 ofu _?(t) fort≥T. In the case where there is no loss of mass inu _? at infinity in a sense to be made precise, we describe the behavior ofu _? as ? goes to zero and we derive an existence result for a solution of (1) after the blow-up timeT in a certain sense. Nonlinear Schrödinger equation with supercritical exponents are also considered.     

Exclusive semi-leptonic decays of bottom mesons in the spectator quark model

We calculate the exclusive semileptonic bottom meson decays \(B \to D(D*) + l^ - + \bar v_l \) in the spectator quark model. The helicity structure of the mesonic current transitionsB→D(D ^*) is matched to the helicity structure of the free quark current transitionsb→c at minimum momentum transferq ²=0. The results are continued toq ²≠=0 by pole-dominated form factors. Our results are compared to recent calculations that use quark model dynamics at maximum momentum transferq _max ² = (M ₁ ?M ₂)². We find agreement atq _max ² . Atq ²=0 there are significant differences between the predictions of the two approaches leading to marked differences in the predictions for the shape of the lepton energy spectrum, the shape of theq ²-distribution, and the helicity composition of the transition measurable in the angular distributions of the decaysD ^*→Dπ and \(W_{virtual}^ - \to l^ - + \bar v_l \) .     

\hat sl(2) \oplus \hat sl(2)/\hat sl(2) coset theory is a Hamiltonian reduction of the \hat D(2|1;\alpha ) superalgebra

It is shown that $\hat sl(2)_{k_1 } \oplus \hat sl(2)_{k_2 } /\hat sl(2)_{k_1 + k_2 } $ coset theory is a quantum Hamiltonian reduction of the exceptional affine Lie superalgebra $\hat D(2|1;\alpha )$ . In addition, the W algebra of this theory is the commutant of the U _q D(2|1;a) quantum group.     

On Endomorphisms of Quantum Tensor Space

We give a presentation of the endomorphism algebra ${\rm End}_{\mathcal {U}_{q}(\mathfrak {sl}_{2})}(V^{\otimes r})$ , where V is the three-dimensional irreducible module for quantum ${\mathfrak {sl}_2}$ over the function field ${\mathbb {C}(q^{\frac{1}{2}})}$ . This will be as a quotient of the Birman–Wenzl–Murakami algebra BMW _r (q) : =  BMW _r (q ^?4, q ² ? q ^?2) by an ideal generated by a single idempotent Φ _q . Our presentation is in analogy with the case where V is replaced by the two-dimensional irreducible ${\mathcal {U}_q(\mathfrak {sl}_{2})}$ -module, the BMW algebra is replaced by the Hecke algebra H _r (q) of type A _r-1, Φ _q is replaced by the quantum alternator in H ₃(q), and the endomorphism algebra is the classical realisation of the Temperley–Lieb algebra on tensor space. In particular, we show that all relations among the endomorphisms defined by the R-matrices on ${V^{\otimes r}}$ are consequences of relations among the three R-matrices acting on ${V^{\otimes 4}}$ . The proof makes extensive use of the theory of cellular algebras. Potential applications include the decomposition of tensor powers when q is a root of unity.     

Construction of kernels of the nonlinear collision integral in the Boltzmann equation using laplace transformation

It is shown that the relation between kernels L _l (v, v ₁) of the linear collision integral and kernels G _l,0 ^l (v, v ₁, v ₂) of the nonlinear collision integral can be reduced to the Laplace transformation. Analytic expressions for nonlinear kernels G _0,0 ⁺⁰ (v, v ₁, v ₂) and G _1,0 ⁺¹ (v, v ₁, v ₂) are determined for hard spheres and pseudo-Maxwellian molecules.     

151,153Eu electron paramagnetic resonance in SrMoO4 and determination of signs of spin Hamiltonian parameters at different temperatures

The electron paramagnetic resonance (EPR) spectra of Eu²⁺ impurity centers in SrMoO₄ crystals have been studied in the temperature range of 1.8, 100–300 K. A hyperfine structure has been simulated for ^151,153Eu of different EPR transitions observed experimentally at different temperatures and external magnetic field orientations. A unique set of all parameters of the spin Hamiltonian for the known sign of the hyperfine interaction parameters A _i has been determined. It has been found that the diagonal parameters |b _n ⁰ | of the spin Hamiltonian decrease with increasing temperature; however, the parameter b ₄ ⁴ increases. The results of the study have demonstrated that |b ₂ ⁰ (T)/P ₂ ⁰ (T)| ～ const for ^151,153Eu in this single crystal.     

Chiral symmetry breaking in the colour dielectric model

Approximating the long-distance gluon dynamics ofSU(3)_colour by colour-dielectric block-spin variables, we obtain an effective QCD theory of a scalar colour-dielectric field and a massive colour-bleached gluon field coupled to light quarks. The massive vector field produces a strong attraction betweenq \(\bar q\) pairs, which leads toq \(\bar q\) condensation when the colour-dielectric field becomes small. We calculate \(\left\langle {\bar \psi \psi } \right\rangle\) and the pion decay constantf _n as a function of the dielectric field expectation value, by evaluating the fermion determinant in a derivative expansion, and integrating out the bosonic variables. We find that the effective quark-gluon coupling,α _s ^eff , including quark effects, is large on the surface of bags, where \(\left\langle {\bar \psi \psi } \right\rangle\) ±0, but decreases inside hadronic bags, where | \(\left\langle {\bar \psi \psi } \right\rangle\) | is decreasing.     

Phase transitions for φ 2 4 quantum fields

Phase transitions for the quantum field interaction λφ⁴+m ₀ ² φ²,m ₀ ² /λ?1 are established in two dimensional space time.     

Extension to velocity dependent gauge transformations

In previous papers it was shown that in phase space a generator of gauge transformations for a singular Lagrangian \(L(q,\dot q)\) is given byG[ε^α]=ε _k ^α φ _α ^k (q,p,t) where φ _α ^k are first class constraints andG is subjected to a stationarity condition. A non-trivial extension from velocity (or momentum) independent gauge transformations to velocity dependent ones is realized, by replacing gauge functions ε^α(t) with momentum dependent functions ε^α(q,p,t), as long asG satisfies the stationarity condition. Inversely, it is proved in a classical framework that, within velocity dependent gauge transformations, all generators of gauge transformations can be expressed in terms of the linear combinations of φ _α ^k .     

Lebensdauer- und Hyperfeinstrukturmessungen an einigen angeregten Zuständen der Konfiguration 4d 9 5p im Pd I-Spektrum mit der Level-crossing-Methode

Lifetimes and hfs coupling constants of some excited states of the 4d ⁹ 5p configuration of Pd I have been determined in a level crossing experiment by observing the field dependence of the polarization of the fluorescence radiation in a magnetic field. From the halfwidths of the measured zero field level crossing signals one obtains the mean lifetimes of the following fine structure states:τ(³P ₁ ⁰ )=(7.46±0.32)nsec;τ(³ P ₂ ⁰ )=(6.9±0.76)nsecτ(³P ₁ ⁰ )=(4.99±0.35)nsec;τ(³ D ₁ ⁰ )=(4.89±0.40)nsecτ((³D ₃ ⁰ )=(6.99±0.49)nsec;τ(³ F ₄ ⁰ )=(7.09±0.46)nsec.Δm=2 crossing signals were detected in the³ P ₁ ⁰ ,³D ₃ ⁰ and³F ₄ ⁰ -states of the odd isotope¹⁰⁵Pd. A detailed analysis of the experimental curves yields the hfs coupling constantsA andB of these states:A(³P ₁ ⁰ )=?(133±2) Mc/sec;B(³ P ₁ ⁰ )=(140±30) Mc/secA(³D ₃ ⁰ )=?(120±10) Mc/sec;B(³ D ₃ ⁰ )=?(660±100) Mc/secA(³F ₄ ⁰ )=?(87±2) Mc/sec;B(³ F ₄ ⁰ )=?(330±30) Mc/sec. A theoretical calculation of the hfs constants is given on the basis of reduced matrix elements. Within the limit of the errors these values agree with the experimental ones. The nuclear electric quadrupole moment deduced from the measuredB values isQ (¹⁰⁵Pd)=(0.8±0.3)·10^?24 cm² (without corrections).     

Laser Raman spectra of mixed crystals of [(NH4)1−x Kx]2 SO4

The Raman spectra of mixed crystals of [(NH₄)_1?x K _x ]₂ SO₄ in the region 50–3400 cm^?1 at 293 K and below 223 K have been reported. At room temperature 293 K, as the concentration of K⁺ ion increases in the crystal up to 50%, the frequencies of the totally symmetric vibrations of SO ₄ ^2? and NH ₄ ⁺ ions increase and thereafter the frequency of SO ₄ ^2? vibration decreases and attains the value in K₂SO₄. This change in frequency up to 50% of potassium concentration is due to the breaking of hydrogen bonds of the type N-H...O. The behaviour of Raman intensities of A _g (v ₁) mode of SO ₄ ^2? for various concentrations (x=0, 0·03, 0·11, 0·5, 0·85) suggest that the phase transition changes from first order type to one of second order. The phase transition in mixed crystals of [(NH₄)_1?x K _x ]₂ SO₄ can be a cooperative phenomenon arising from a coupling between (NH₄)⁺ ions through hydrogen bonds with the distorted SO ₄ ^2? ions in the low temperature phase.     

Vacuum energy ingϕ d /4 -theory forg→∞

In the nonlocalg? _d ^/4 (d≧1) and localg? ₂ ⁴ theory theS-matrix is obtained in a form of the functional integral which is proved to exist. The density of vacuum energy $$E(g) = - \mathop {\lim }\limits_{V \to \infty } \frac{1}{V}\ln \left\langle {0\left| {S_V (g)} \right|0} \right\rangle $$ is investigated. It is proved to be analytic through the whole complexg-plane except for the negative real axis and pointg=0. Its asymptotic behaviour forg→∞ is found.