Knot and Conformal Field Theory Approach in Molecular and Nuclear Physics

Abstract

It is shown that the eigenvalue of a quadratic Casimir operator of quantum universal enveloping (QUE) algebra of SUz explains successfully the observed rotational spectra of a molecule. A similar idea is applied to two nuclei. The problem of dissociation (binding) energy for the molecules (nuclei) is discussed shortly. Witten!) has developed the theory of QUE algebra in a set of three papers. The theory is generally covariant and gauge invariant. He gave a q deformed Casimir operator of SU2 quantum group as an example, with which we concern ourselves in this paper. Most of the tools 2 ) to prove the theoretical results are familiar with the high-energy physicists, except, perhaps, for the knot, braid and link theory3) which is developed further in recent years, in connection with the exact solvability4) of many models in solid stale physics and statistical mechanics. We wish to show that, in spite of its historical origin, the result is quite useful to interpret the rotational spectra of molecules and nuclei. In this paper we shall give some examples in both fields and wish to discuss shortly the dissociation (binding) energy for molecules (nuclei). From a practical point of view it is not necessary to understand the whole detail of the theory. We shall begin with the eigenvalue of the quadratic Casimir operator of QUE algebra for SU2 and state the physical significance of it in relevance to the available information. It is given by