Algebraic realization of rotational dynamics
Abstract
It is shown that the dynamics of a quantum rotor can be realized in terms of the SU(3) → SO(3) group algebra. Specifically, an analytic result is given for mapping from the hamiltonian of a trixial rotor to its algebraic image. Under the mapping invariants of the rotor are carried into Casimir invariants of the algebraic theory. Results for spectra and transition rates and various sums are given to demonstrate the effectiveness of the mapping. The theory gives physical significance to operators that were first introduced by Racah as a means for resolving the SU(3) → SO(3) state labelling problem. As the SU(3) → SO(3) structure is common to the rotational limit of several nuclear models, the theory also offers an opportunity to explore in a new way the microscopic underpinnings of rotational phenomena in nuclei. © 1987.