The Composite Particle Representation Theory: (I) The Composite Particle Representation Transformation

Abstract

A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a generalized transformation. Using this generalization, we were able to construct a special representation called the “Composite Particle Representation”. In the composite, particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical representation which includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons from the quark point of view and the Interacting Boson Model in nuclei.