Properties of the symplecton calculus

Lawrence C. Biedenharn, Max A. Lohe, Masao Nomura

The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.

F. A. Barone, Renato Grassini

Max A. Lohe, Lawrence C. Biedenharn, James D. Louck

Weyl-ordered polynomials, which have been used recently to solve quantum-mechanical models, are shown to be equivalent to symplecton polynomials defined previously as components of a tensor operator in SU(2). These polynomials are shown to be expressible in terms of hypergeometric functions of argument -1, providing thereby a direct derivation of their properties.

Maurice A. de Gosson

D. J. Simms, L. Castel

Lawrence C. Biedenharn, James D. Louck

Abstract : The paper demonstrates by explicit construction a primitive minimal realization of the SU(2) approximately equal to Sp(2) symmetry group in terms of a single boson operator. Our construction denies the usual boson rule, and as such constitutes a true generalization of the concept of boson. The resulting inherently conjugation symmetric structure is denoted as a symplecton. (Author)