A note on the superselection rules for spin- [formula omitted] bosons

Abstract

<dm:abstracts xmlns:dm="http://www.elsevier.com/xml/dm/dtd"><ce:abstract xmlns:ce="http://www.elsevier.com/xml/common/dtd" view="all" class="author" id="aep-abstract-id5"><ce:section-title>Publisher Summary</ce:section-title><ce:abstract-sec view="all" id="aep-abstract-sec-id6"><ce:simple-para id="fsabs015" view="all">In the algebraic method, we see that one characteristic of molecular highly excited vibration is its immense number and high density of states. These quanta are bosons and can populate the various modes and transfer among them. Due to the interaction among the quanta, many quantum numbers are destroyed. The destruction of quantum numbers, in another aspect, implies that their classical analogs, the actions which are continuous variables, have to be employed for the description of highly excited vibration. In classical mechanics, angle is a companion of action. Hence, in the study of molecular highly excited vibration, both action and angle are important physical quantities. Albeit at high excitation, most of the quantum numbers are destroyed and are no longer constants of motion, there are still some good quantum numbers left. These remaining quantum numbers are called the polyad numbers. We note that polyad numbers are only approximate. They are, in fact, conserved only in certain dynamical processes. This is because as time elapses, the dynamics will become very complicated and the resonance forms may vary so that the polyad number as an operator may no longer commute with the full Hamiltonian. Diabatic correlation, formal quantum numbers, and ordering of levels are other topics that are covered. The switching-off of the seven resonances of formaldehyde and the labelings of the various levels via the diabatic correlation is shown in the graph. In acetylene case, the five in-plane motions are studied in detail. The cases of formaldehyde and acetylene show that for the highly excited vibration, by the diabatic correlation, we can employ the quantum numbers of the zeroth-order Hamiltonian, called the formal quantum numbers, to reconstruct its levels in a very regular pattern. Although, due to resonances, these formal quantum numbers are no longer the constants of motion, they are still useful for the ordering of the levels. The background of diabatic correlation shows that besides polyad numbers, other approximately conserved quantities. Approximately conserved quantum numbers are studied with relevant explanation and graphs. DCN case is also studied. The difference between approximate and formal quantum numbers is shown in the table. The density cospace and Lyapunov exponents are calculated for all the exponents studied and are also shown.</ce:simple-para></ce:abstract-sec></ce:abstract></dm:abstracts>