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

Squeezed States and Particle Production in High Energy Collisions

Using the `quantum optical approach' we propose a model of multiplicity distributions in high energy collisions based on squeezed coherent states. We show that the k-mode squeezed coherent state is the most general one in describing hadronic mulitiplicity distributions in particle collision processes, describing not only $p \bar p$ collisions but $e^{+}e^{-}$, $\nu p$ and diffractive collisions as well. The reason for this phenomenological fit has been gained by working out a microscopic theory in which the squeezed coherent sources arise naturally if one considers the Lorentz squeezing of hadrons and works in the covariant phase space formalism .Comment: 7 pages, 4 Figures (can be obtained from author by snail mail

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