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International Journal of Modern Physics E

THE COMPOSITE PARTICLE REPRESENTATION APPROACH TO BOSON MAPPING

Cheng-Li Wu

Published Jan 1, 1993• 3 citations
Publisher

Abstract

The composite particle representation theory (CPRT) and its application to boson mapping is reviewed. The symmetry limits of the Fermion Dynamical Symmetry Model (FDSM) is employed as a solvable model to test the validity of various boson mapping approaches. It is shown that the composite particle representation approach is a very powerful tool for boson mapping. The spurious state problem is also discussed.

DOI
10.1142/s0218301393000492

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The composite particle representation theory (CPRT) and its application to boson mapping is reviewed. The symmetry limits of the Fermion Dynamical Symmetry Model (FDSM) is employed as a solvable model to test the validity of various boson mapping approaches. It is shown that the composite particle representation approach is a very powerful tool for boson mapping. The spurious state problem is also discussed.
The composite particle representation theory (CPRT) proposed by Wu and Feng is examined by comparing its results to the shell-model calculations of Wildenthal and Chung for the s-d shell nuclei 20O^{20}\mathrm{O}20O, 20F^{20}\mathrm{F}20F, and 20Ne^{20}\mathrm{Ne}20Ne. Each identical nucleon pair is treated in the CPRT as a boson. In all cases, the CPRT results are identical to the shell model. It was found that by evaluating the normalizations and the error sums of the CPRT wave functions, the spurious states, a subject of vital importance for any mapping theory, can be and are correctly removed. This shows that the composite particle representation is equivalent to the conventional representation in quantum mechanics. Thus the CPRT can provide an exact theoretical framework to treat particle clusters as ideal bosons (or fermions, depending on the nature of the clusters) in a many-body system, and is particularly useful for any quantum systems where clusterization dominates.
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.