Physics – Quantum Physics
Scientific paper
1997-12-11
J.Math.Phys. 39 (1998) 2418-2427
Physics
Quantum Physics
17 pages,no figure. to appear in J. Math.Phys
Scientific paper
10.1063/1.532295
It has been shown that the Cartan subalgebra of $W_{\infty}$- algebra is the space of the two-variable, definite-parity polynomials. Explicit expressions of these polynomials, and their basic properties are presented. Also has been shown that they carry the infinite dimensional irreducible representation of the $su(1,1)$ algebra having the spectrum bounded from below. A realization of this algebra in terms of difference operators is also obtained. For particular values of the ordering parameter $s$ they are identified with the classical orthogonal polynomials of a discrete variable, such as the Meixner, Meixner-Pollaczek, and Askey-Wilson polynomials. With respect to variable $s$ they satisfy a second order eigenvalue equation of hypergeometric type. Exact scattering states with zero energy for a family of potentials are expressed in terms of these polynomials. It has been put forward that it is the \.{I}n\"{o}n\"{u}-Wigner contraction and its inverse that form bridge between the difference and differential calculus.
No associations
LandOfFree
Ordered Products, $W_{\infty}$-Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ordered Products, $W_{\infty}$-Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ordered Products, $W_{\infty}$-Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-527510