Dirac-Schr\"odinger equation for quark-antiquark bound states and derivation of its interaction kerne

The four-dimensional Dirac-Schr\"odinger equation satisfied by quark-antiquark bound states is derived from Quantum Chromodynamics. Different from the Bethe-Salpeter equation, the equation derived is a kind of first-order differential equations of Schr\"odinger-type in the position space. Especially, the interaction kernel in the equation is given by two different closed expressions. One expression which contains only a few types of Green's functions is derived with the aid of the equations of motion satisfied by some kinds of Green's functions. Another expression which is represented in terms of the quark, antiquark and gluon propagators and some kinds of proper vertices is derived by means of the technique of irreducible decomposition of Green's functions. The kernel derived not only can easily be calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations. Furthermore, it is shown that the four-dimensinal Dirac-Schr\"odinger equation and its kernel can directly be reduced to rigorous three-dimensional forms in the equal-time Lorentz frame and the Dirac-Schr\"odinger equation can be reduced to an equivalent Pauli-Schr\"odinger equation which is represented in the Pauli spinor space. To show the applicability of the closed expressions derived and to demonstrate the equivalence between the two different expressions of the kernel, the t-channel and s-channel one gluon exchange kernels are chosen as an example to show how they are derived from the closed expressions. In addition, the connection of the Dirac-Schr\"odinger equation with the Bethe-Salpeter equation is discussed

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo

Multi-channel phase-equivalent transformation and supersymmetry

Phase-equivalent transformation of local interaction is generalized to the multi-channel case. Generally, the transformation does not change the number of the bound states in the system and their energies. However, with a special choice of the parameters, the transformation removes one of the bound states and is equivalent to the multi-channel supersymmetry transformation recently suggested by Sparenberg and Baye. Using the transformation, it is also possible to add a bound state to the discrete spectrum of the system at a given energy $E<0$ if the angular momentum at least in one of the coupled channels $l\ge 2$.Comment: 9 pages, revtex; to be published in Phys. At. Nucl. (Oct. 2000

Lepton charge and neutrino mixing in pion decay processes

We consider neutrino mixing and oscillations in quantum field theory and compute the neutrino lepton charge in decay processes where neutrinos are generated. We also discuss the proper definition of flavor charge and states and clarify the issues of the possibility of different mass parameters in field mixing.Comment: 13 page

Electromagnetic Meson Form Factors in the Salpeter Model

We present a covariant scheme to calculate mesonic transitions in the framework of the Salpeter equation for $q\bar{q}$-states. The full Bethe Salpeter amplitudes are reconstructed from equal time amplitudes which were obtained in a previous paper\cite{Mue} by solving the Salpeter equation for a confining plus an instanton induced interaction. This method is applied to calculate electromagnetic form factors and decay widths of low lying pseudoscalar and vector mesons including predictions for CEBAF experiments. We also describe the momentum transfer dependence for the processes $\pi^0,\eta,\eta'\rightarrow\gamma\gamma^*$.Comment: 22 pages including 10 figure

Large Possible retardation effects of quark confinement on the meson spectrum II

We present the results of a study of heavy-light-quark bound states in the context of the reduced Bethe-Salpeter equation with relativistic vector and scalar interactions. We find that satisfactory fits may also be obtained when the retarded effect of the quark-antiquark interaction is concerned.Comment: 11 pages, RevTex, to appear in PR

On the Deformation of a Hyperelastic Tube Due to Steady Viscous Flow Within

In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena. The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the walls of a long vessel allow the structure to be treated as a pressure vessel. The constitutive equation for the microtube is prescribed via the strain energy functional for an incompressible, isotropic Mooney--Rivlin material. We employ both the thin- and thick-walled formulations of the pressure vessel theory, and derive the static relation between the pressure load and the deformation of the structure. We harness the latter to determine the flow rate--pressure drop relationship for non-Newtonian flow in thin- and thick-walled soft hyperelastic microtubes. Through illustrative examples, we discuss how a hyperelastic tube supports the same pressure load as a linearly elastic tube with smaller deformation, thus requiring a higher pressure drop across itself to maintain a fixed flow rate.Comment: 19 pages, 3 figures, Springer book class; v2: minor revisions, final form of invited contribution to the Springer volume entitled "Dynamical Processes in Generalized Continua and Structures" (in honour of Academician D.I. Indeitsev), eds. H. Altenbach, A. Belyaev, V. A. Eremeyev, A. Krivtsov and A. V. Porubo

Possible retardation effects of quark confinement on the meson spectrum

The reduced Bethe-Salpeter equation with scalar confinement and vector gluon exchange is applied to quark-antiquark bound states. The so called intrinsic flaw of Salpeter equation with static scalar confinement is investigated. The notorious problem of narrow level spacings is found to be remedied by taking into consideration the retardation effect of scalar confinement. Good fit for the mass spectrum of both heavy and light quarkomium states is then obtained.Comment: 14 pages in LaTex for

Functional characterization of a melon alcohol acyl-transferase gene family involved in the biosynthesis of ester volatiles. Identification of the crucial role of a threonine residue for enzyme activity

Volatile esters, a major class of compounds contributing to the aroma of many fruit, are synthesized by alcohol acyl-transferases (AAT). We demonstrate here that, in Charentais melon (Cucumis melo var. cantalupensis), AAT are encoded by a gene family of at least four members with amino acid identity ranging from 84% (Cm-AAT1/Cm-AAT2) and 58% (Cm-AAT1/Cm-AAT3) to only 22% (Cm-AAT1/Cm-AAT4). All encoded proteins, except Cm-AAT2, were enzymatically active upon expression in yeast and show differential substrate preferences. Cm-AAT1 protein produces a wide range of short and long-chain acyl esters but has strong preference for the formation of E-2-hexenyl acetate and hexyl hexanoate. Cm-AAT3 also accepts a wide range of substrates but with very strong preference for producing benzyl acetate. Cm-AAT4 is almost exclusively devoted to the formation of acetates, with strong preference for cinnamoyl acetate. Site directed mutagenesis demonstrated that the failure of Cm-AAT2 to produce volatile esters is related to the presence of a 268-alanine residue instead of threonine as in all active AAT proteins. Mutating 268-A into 268-T of Cm-AAT2 restored enzyme activity, while mutating 268-T into 268-A abolished activity of Cm-AAT1. Activities of all three proteins measured with the prefered substrates sharply increase during fruit ripening. The expression of all Cm-AAT genes is up-regulated during ripening and inhibited in antisense ACC oxidase melons and in fruit treated with the ethylene antagonist 1-methylcyclopropene (1-MCP), indicating a positive regulation by ethylene. The data presented in this work suggest that the multiplicity of AAT genes accounts for the great diversity of esters formed in melon

Functional Lagrange formalism for time-non-local Lagrangians

We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.Comment: 13 pages, 2 figure