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.     

Representation of osp (2, 2) q (2) andS-matrix of super sine-Gordon theory

We investigate the representations of the osp (2, 2) _q ⁽²⁾ algebra, which leads to theS-matrix of super sine-Gordon theory. TheS-matrix has been derived from supersymmetric conformal field theory with some assumptions. We show that the conjecturedS-matrix can be derived from the representation theory using a correspondence between the representations of osp (1, 2) _q and those of sl(2) _q .     

Spin-1 particle in a homogeneous magnetic field

The Corben-Schwinger theory gives imaginary values of the energy, forS ₃ ² =1 states, in very intensive magnetic fields. The theory proposed by the author, which is most satisfactory in the nonrelativistic approximation, does not have this defect forS ₃ ² =1 states, but it appears forS ₃ ² =0 states.     

Interaction of Zn atoms in the 1 S and 3 P states with N2 molecules in the X 1Σ g + and A 3Σ u + states at moderate distances between the atom and molecule

An asymptotic method was used to derive analytical expressions for the matrix elements of interaction between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ electronic states and the Zn atom in the ¹ S and ³ P states. Quadrupole-quadrupole, dispersion, and exchange interactions were taken into consideration. The character of the set of diabatic vibronic potential energy surfaces of the system suggests that the energy transfer in the process N₂(A ³Σ _u ⁺ ) + Zn(¹ S) → N₂(X ¹Σ _g ⁺ ) + Zn(³ P) may prove to be rather effective.     

Electron-vibrational energy exchange in collisions of electronically excited N2(A 3Σ u + ) molecules with Zn(X 1 S) atoms

The interaction matrix between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ states and the Zn atom in the ¹ S and ³ P states calculated earlier by the asymptotic method was used to find the rate constants for the electron-vibrational energy exchange N₂(A ³Σ _u ⁺ , v) + Zn(¹ S) → N₂(X ¹Σ ₈ ⁺ , v′) + Zn(³ P). The calculations were performed by the transition state method, and the probabilities of transitions between intersecting electron-vibrational terms of the system in motion along the reaction coordinate were determined by the Landau-Zener equation. The calculated electron excitation transfer constants between N₂(A ³Σ _u ⁺ , v = 1, 0) and Zn(¹ S) over the temperature range 300–900 K were on the order of 10^?11?10^?12 cm³/s.     

Gyromagnetic ratios of excited states in186W

The gyromagnetic ratios of the 4 ₁ ⁺ , 6 ₁ ⁺ , and 2 ₂ ⁺ states in¹⁸⁶W were measured relative to that of the 2 ₁ ⁺ level by means of the transient field implantation perturbedγ-ray angular distribution technique. The nuclei in the states of interest were Coulomb excited using a beam of 220-MeV⁶³Cu projectiles and recoiled swiftly through a thin, polarized Fe foil. The present measurements yielded ratiosg(4 ₁ ⁺ )/g(2 ₁ ⁺ )=1.04±0.07,g(6 ₁ ⁺ )/g(2 ₁ ⁺ )=1.03 ±0.20 andg(2 ₂ ⁺ )/g(2 ₁ ⁺ )=0.63±0.13. The sizable disparity between the measuredg-factors of the ground- and excited-band is examined within the context of the interacting boson approximation model.     

The quark configurationsS 6 andS 4 P 2 in the bag model

The spectrum and eigenfunctions of deuteronlike states in the quark bag for the configurationsS ⁶ andS ⁴ P ² have been studied. The complete tables of the fractional parentage coefficients (f.p.c.) for these configurations in thej-j andL-S coupling schemes are presented. The universal method of calculation of the f.p.c. which is based on the complementarity of the unitary and permutation group, is considered. The method enable one to calculate the Clebsh-Gordon coefficients and the invariant symbols of the noted groups. It is shown that the lowest energy state of the configurationS ₁ ^2/4 P ₃ ^2/2 resembles the partial wave³ D ₁ and can, therefore, be coupled to it in a deuteron. On the contrary, the lowest states in the configurationsS ₁ ^2/6 andS ₁ ^2/4 P ₁ ^2/2 resemble the³ S ₁-wave.     

Description of the properties of the low-lying energy states in 100Mo with IBM2

The properties of the low-lying energy states for the 100Mo isotope is investigated within the framework of the proton-neutron interacting model IBM2.By considering the relative energy of the d proton boson to be diferent from that of the neutron boson and taking into account the dipole interacting among like-boson LπLπand LνLν,the low-lying energy spectrum is reproduced well.Particularly,the relative position of the energies for 2+1,0+2,2+2 and 4+1states shifted correctly fit the experimental data.The electromagnetic properties,including the key observable B(E2)reduced transition branching ratios and the E2 reduced matrix elements of the experimental data,are well described.Our calculations show possible shape coexistence in the 100Mo nucleus.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

The CLR Inequality for Dominated Semigroups

The Cwikel-Lieb-Rozenbljum inequality estimating the number of bound states of a quantum Hamiltonian operator is proved for semigroups \(S(t) = \mathrm {e}_{0}^{-tH}\) , \(t\geqslant 0\) , on L ²(μ) for a σ-finite measure μ, such that S is dominated by a semigroup |S| of point wise positive operators on L ²(μ).     

Combinatorics of Generalized Bethe Equations

A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over ${\mathbb{Z}^M}$ Z M , and on the other hand, they count integer points in certain M-dimensional polytopes.     

The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σ _u ^?1 (c ⁴Σ _u ^? ), v vibrational states of the O ₂ ⁺ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ₀ = 0.054 meV and Γ₁ = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O₂ molecule. About 99% of the O ₂ ⁺ ions in the 2σ _u ^?1 (c ⁴Σ _u ^? ), v states were found to decompose to the O(¹ D) + O⁺(⁴ S) dissociation products.     

Z c (4025) as the hadronic molecule with hidden charm

We have studied the loosely bound $D^{*}\bar{D}^{*}$ system. Our results indicate that the recently observed charged charmonium-like structure Z _c (4025) can be an ideal $D^{*}\bar{D}^{*}$ molecular state. We have also investigated its pionic, dipionic, and radiative decays. We stress that both the scalar isovector molecular partner Z _c0 and three isoscalar partners ${\tilde{Z}}_{c0,c1,c2}$ should also exist if Z _c (4025) is a $D^{*}\bar{D}^{*}$ molecular state in the framework of the one-pion-exchange model. Z _c0 can be searched for in the channel e ⁺ e ^?→Y→Z _c0(4025)(ππ)_P-wave where Y can be Y(4260) or any other excited 1^?? charmonium or charmonium-like states such as Y(4360), Y(4660), etc. The isoscalar $D^{*}\bar{D}^{*}$ molecular states ${\tilde{Z}}_{c0,c2}$ with 0⁺(0⁺⁺) and 0⁺(2⁺⁺) can be searched for in the three pion decay channel $e^{+}e^{-}\to Y \to {\tilde{Z}}_{c0,c2} (3\pi)^{I=0}_{\text{P-wave}}$ . The isoscalar molecular state ${\tilde{Z}}_{c1}$ with 0^?(1^+?) can be searched for in the channel ${\tilde{Z}}_{c1}\eta$ . Experimental discovery of these partner states will firmly establish the molecular picture.     

A semi-classical trace formula for Schrödinger operators

LetS _?=??Δ+V, withV smooth. If 0<E ²V(x), the spectrum ofS _? nearE ² consists (for ? small) of finitely-many eigenvalues,λ _j (?). We study the asymptotic distribution of these eigenvalues aboutE ² as ?→0; we obtain semi-classical asymptotics for $$\sum\limits_j {f\left( {\frac{{\sqrt {\lambda _j (\hbar )} - E}}{\hbar }} \right)} $$ with \(\hat f \in C_0^\infty \) , in terms of the periodic classical trajectories on the energy surface \(B_E = \left\{ {\left| \xi \right|^2 + V(x) = E^2 } \right\}\) . This in turn gives Weyl-type estimates for the counting function \(\# \left\{ {j;\left| {\sqrt {\lambda _j (\hbar )} - E} \right| \leqq c\hbar } \right\}\) . We make a detailed analysis of the case when the flow onB _E is periodic.     

Search for Θ+(1540) in exclusive proton-induced reaction p + C(N) \to \Theta ^ + \bar \kappa ^0 + C(N) at the energy of 70 GeV

A search for narrow Θ⁺(1540), a candidate for a pentaquark baryon with positive strangeness, has been performed in an exclusive proton-induced reaction $p + C(N) \to \Theta ^ + \bar \kappa ^0 + C(N)$ on carbon nuclei or quasifree nucleons at $E_{beam} = 70GeV(\sqrt s = 11.5GeV)$ studying nK ⁺, pK _S ⁰ , and pK _L ⁰ decay channels of Θ⁺(1540) in four different final states of the $\Theta ^ + \bar K^0 $ system. In order to assess the quality of the identification of the final states with neutron or K _L ⁰ , we reconstructed Λ(1520) → nK _S ⁰ and ? → K _L ⁰ K _S ⁰ decays in the calibration reactions p + C(N) → Λ (1520)K ⁺+C(N) and p+C(N) → p?+C(N). We found no evidence for a narrow pentaquark peak in any of the studied final states and decay channels. Assuming that the production characteristics of the $\Theta ^ + \bar K^0 $ system are not drastically different from those of the Λ(1520)K ⁺ and p? systems, we established upper limits on the cross-section ratios $\sigma (\Theta ^ + \bar K^0 )/\sigma (\Lambda (1520)K^ + ) < 0.02$ and $\sigma (\Theta ^ + \bar K^0 )/\sigma (p\phi ) < 0.15$ at 90% C.L. and a preliminary upper limit for the forward-hemisphere cross section $\sigma (\Theta ^ + \bar K^0 )$ nb/nucleon.     

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:

1. The regularizedS ^δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
2. The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?^δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
3. The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ₁=δ₂=δ₃=0.
4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

Charmed quark component of the photon wave function

We determine the $c\bar c$ component of the photon wave function on the basis of (i) the data on the transitions e ⁺ e ^? → J/ψ(3096), ψ(3686), ψ(4040), ψ(4415), (ii) partial widths of the two-photon decays η _c0(2979), χ _c0(3415), χ _c2(3556) → γγ, and (iii) wave functions of the charmonium states obtained by solving the Bethe-Salpeter equation for the $c\bar c$ system. Using the obtained $c\bar c$ component of the photon wave function, we calculate the γγ-decay partial widths for radial excitation of the 2S state, η _c0(3594) → γγ, and 2P states χ _c0(3849), χ _c2(3950) → γγ.