Masses and Internal Structure of Mesons in the String Quark Model

The relativistic quantum string quark model, proposed earlier, is applied to all mesons, from pion to $\Upsilon$, lying on the leading Regge trajectories (i.e., to the lowest radial excitations in terms of the potential quark models). The model describes the meson mass spectrum, and comparison with measured meson masses allows one to determine the parameters of the model: current quark masses, universal string tension, and phenomenological constants describing nonstring short-range interaction. The meson Regge trajectories are in general nonlinear; practically linear are only trajectories for light-quark mesons with non-zero lowest spins. The model predicts masses of many new higher-spin mesons. A new $K^*(1^-)$ meson is predicted with mass 1910 Mev. In some cases the masses of new low-spin mesons are predicted by extrapolation of the phenomenological short-range parameters in the quark masses. In this way the model predicts the mass of $\eta_b(1S)(0^{-+})$ to be $9500\pm 30$ MeV, and the mass of $B_c(0^-)$ to be $6400\pm 30$ MeV (the potential model predictions are 100 Mev lower). The relativistic wave functions of the composite mesons allow one to calculate the energy and spin structure of mesons. The average quark-spin projections in polarized $\rho$-meson are twice as small as the nonrelativistic quark model predictions. The spin structure of $K^*$ reveals an 80% violation of the flavour SU(3). These results may be relevant to understanding the ``spin crises'' for nucleons.Comment: 30 pages, REVTEX, 6 table

Expectation values of single-particle operators in the random phase approximation ground state

We developed a method for computing matrix elements of single-particle operators in the correlated random phase approximation ground state. Working with the explicit random phase approximation ground state wavefunction, we derived practically useful and simple expression for a molecular property in terms of random phase approximation amplitudes. The theory is illustrated by the calculation of molecular dipole moments for a set of representative molecules.Comment: Accepted to J.Chem.Phy

Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism

We consider the algebra of spatial diffeomorphisms and gauge transformations in the canonical formalism of General Relativity in the Ashtekar and ADM variables. Modifying the Poisson bracket by including surface terms in accordance with our previous proposal allows us to consider all local functionals as differentiable. We show that closure of the algebra under consideration can be achieved by choosing surface terms in the expressions for the generators prior to imposing any boundary conditions. An essential point is that the Poisson structure in the Ashtekar formalism differs from the canonical one by boundary terms.Comment: 19 pages, Latex, amsfonts.sty, amssymb.st

Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

Putting an Edge to the Poisson Bracket

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed. We introduce a new Poisson bracket which differs from the usual ``bulk'' Poisson bracket with a boundary term and show that the Jacobi identity is satisfied. The result is geometrized on an abstract world volume manifold. The method is suitable for studying systems with a spatial edge like the ones often considered in Chern-Simons theory and General Relativity. Finally, we discuss how the boundary terms may be related to the time ordering when quantizing.Comment: 36 pages, LaTeX. v2: A manifest formulation of the Poisson bracket and some examples are added, corrected a claim in Appendix C, added an Appendix F and a reference. v3: Some comments and references adde