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Progress of Theoretical Physics

Application of the Canonical Theory of Mixed State to the Description of Bound State of the Nucleus. II

A. Kuriyama, João da Providência, Masatoshi Yamamura

Published Apr 1, 1992• 0 citations
Publisher

Abstract

The theory developed in Part I of this series of papers is adapted to a schematic model, the Lipkin model. In this case, we can introduce a set of canonical variables satisfying automatically the constraints and obtain an exact boson representation of the Lipkin model after a canonical quantization. However, when the constraints themselves are also quantized, the physical ingredients of the constraints are revealed under a completely different perspective.

DOI
10.1143/ptp.87.911

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The theory developed in Part I of this series of papers is adapted to a schematic model, the Lipkin model. In this case, we can introduce a set of canonical variables satisfying automatically the constraints and obtain an exact boson representation of the Lipkin model after a canonical quantization. However, when the constraints themselves are also quantized, the physical ingredients of the constraints are revealed under a completely different perspective.
With the use of the basic idea of the boson mapping method, a new boson realization, which is suitable for the Lipkin model, is proposed. This realization is different from the forms which are obtained with the Holstein-Primakoff and the Schwinger boson representations for the su(2) spin system. Further, with the aid of the basic idea of the TDHF method in canonical form, a method analysing the Lipkin model in the framework of classical mechanics is developed. The condition for the solution of the Hamilton equation of motion is discussed.