Noncentral extensions as anomalies in classical dynamical systems

A two cocycle is associated to any action of a Lie group on a symplectic manifold. This allows to enlarge the concept of anomaly in classical dynamical systems considered by F. Toppan [in J. Nonlinear Math. Phys. 8, no.3 (2001) 518-533] so as to encompass some extensions of Lie algebras related to noncanonical actions.Comment: arxiv version is already officia

Light Hadron Spectroscopy and Decay at BESIII

Light hadron spectroscopy plays an important role in understanding the decay dynamics of unconventional hadronic states, such as strangeonium and glueballs. BESIII provides an ideal avenue to search for these exotic states thanks to a huge amount of data recorded at various energy points in the tau-charm mass region including J/psi resonance. This report summarizes recent results of the BESIII experiment related to the glueballs and strangeonium-like states.Comment: 6 pages, 5 figures, Conference proceeding of FPCP-201

Trapped interacting two-component bosons

In this paper we solve one dimensional trapped SU(2) bosons with repulsive $\delta$-function interaction by means of Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic methods. We show that the ground state is an isospin "ferromagnetic" state which differs from spin-1/2 fermions system. There exist three quasi-particles in the excitation spectra, and both holon-antiholon and holon-isospinon excitations are gapless for large systems. The thermodynamics equilibrium of the system at finite temperature is studied by thermodynamic Bethe ansatz. The thermodynamic quantities, such as specific heat etc. are obtained for the case of strong coupling limit.Comment: 15 pages, 9 figure

Generalized q-Oscillators and their Hopf Structures

We study the relationships among the various forms of the $q$ oscillator algebra and consider the conditions under which it supports a Hopf structure. We also present a generalization of this algebra together with its corresponding Hopf structure. Its multimode extensions are also considered.Comment: 14 page

Realizations of the qq-Heisenberg and qq-Virasoro Algebras

We give field theoretic realizations of both the $q$-Heisenberg and the $q$-Virasoro algebra. In particular, we obtain the operator product expansions among the current and the energy momentum tensor obtained using the Sugawara construction.Comment: 9 page

Initial Conditions for Semiclassical Field Theory

Semiclassical approximation based on extracting a c-number classical component from quantum field is widely used in the quantum field theory. Semiclassical states are considered then as Gaussian wave packets in the functional Schrodinger representation and as Gaussian vectors in the Fock representation. We consider the problem of divergences and renormalization in the semiclassical field theory in the Hamiltonian formulation. Although divergences in quantum field theory are usually associated with loop Feynman graphs, divergences in the Hamiltonian approach may arise even at the tree level. For example, formally calculated probability of pair creation in the leading order of the semiclassical expansion may be divergent. This observation was interpretted as an argumentation for considering non-unitary evolution transformations, as well as non-equivalent representations of canonical commutation relations at different time moments. However, we show that this difficulty can be overcomed without the assumption about non-unitary evolution. We consider first the Schrodinger equation for the regularized field theory with ultraviolet and infrared cutoffs. We study the problem of making a limit to the local theory. To consider such a limit, one should impose not only the requirement on the counterterms entering to the quantum Hamiltonian but also the requirement on the initial state in the theory with cutoffs. We find such a requirement in the leading order of the semiclassical expansion and show that it is invariant under time evolution. This requirement is also presented as a condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur

One dimensional SU(3) bosons with δ\delta function interaction

In this paper we solve one dimensional SU(3) bosons with repulsive $\delta$-function interaction by means of Bethe ansatz method. The features of ground state and low-lying excited states are studied by both numerical and analytic methods. We show that the ground state is a SU(3) color ferromagnetic state. The configurations of quantum numbers for the ground state are given explicitly. For finite $N$ system the spectra of low-lying excitations and the dispersion relations of four possible elementary particles (holon, antiholon, $\sigma$-coloron and $\omega$-coloron) are obtained by solving Bethe-ansatz equation numerically. The thermodynamic equilibrium of the system at finite temperature is studied by using the strategy of thermodynamic Bethe ansatz, a revised Gaudin-Takahashi equation which is useful for numerical method are given . The thermodynamic quantities, such as specific heat, are obtain for some special cases. We find that the magnetic property of the model in high temperature regime is dominated by Curie's law: $\chi\propto 1/T$ and the system has Fermi-liquid like specific heat in the strong coupling limit at low temperature.Comment: RevTex 28 pages, 10 figure