Jordan-Schwinger realizations of three-dimensional polynomial algebras

A three-dimensional polynomial algebra of order $m$ is defined by the commutation relations $[P_0, P_\pm]$ $=$ $\pm P_\pm$, $[P_+, P_-]$ $=$ $\phi^{(m)}(P_0)$ where $\phi^{(m)}(P_0)$ is an $m$-th order polynomial in $P_0$ with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders $l$ and $m$ can be combined to give two distinct $(l+m+1)$-th order polynomial algebras. This procedure follows from a generalization of the well known Jordan-Schwinger method of construction of $su(2)$ and $su(1,1)$ algebras from two mutually commuting boson algebras.Comment: 10 pages, LaTeX2

Aspects of coherent states of nonlinear algebras

Various aspects of coherent states of nonlinear $su(2)$ and $su(1,1)$ algebras are studied. It is shown that the nonlinear $su(1,1)$ Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived.Comment: 22 Pages, 30 Figure

Isospin Squeezed States, Disoriented Chiral condensates and Pion Production: A Dynamic Group Theoretical Approach

We make a complete dynamical study of Isotopic spin conservation effects on the multiplicity distributions of both hard and soft pions emitted in a quark gluon plasma undergoing a non-equilibrium phase transition.Comment: 21 pages, 9 figures, RevTeX4 macr

Order-chaos transitions in field theories with topological terms: a dynamical systems approach

We present a comparative study of the dynamical behaviour of topological systems of recent interest, namely the non-Abelian Chern-Simons Higgs system and the Yang-Mills Chern-Simons Higgs system. By reducing the full field theories to temporal differential systems using the assumption of spatially homogeneous fields , we study the Lyapunov exponents for two types of initial conditions. We also examine in minute detail the behaviour of the Lyapunov spectra as a function of the various coupling parameters in the system. We compare and contrast our results with those for Abelian Higgs, Yang-Mills Higgs and Yang-Mills Chern-Simons systems which have been discussed by other authors recently. The role of the various terms in the Hamiltonians for such systems in determining the order-disorder transitions is emphasized and shown to be counter-intuitive in the Yang-Mills Chern-Simons Higgs systems.Comment: 19 pages,15 figures available in hard copy from C. Mukku, and through e-mail from [email protected]. To appear in J. Phys.