Beyond the Schwinger boson representation of the su(2)-algebra. I -- New boson representation based on the su(1,1)-algebra and its related problems with application

摘要

With the use of two kinds of boson operators, a new boson representation ofthe su(2)-algebra is proposed. The basic idea comes from the pseudosu(1,1)-algebra recently given by the present authors. It forms a strikingcontrast to the Schwinger boson representation of the su(2)-algebra which isalso based on two kinds of bosons. This representation may be suitable fordescribing time-dependence of the system interacting with the externalenvironment in the framework of the thermo field dynamics formalism, i.e., thephase space doubling. Further, several deformations related to thesu(2)-algebra in this boson representation are discussed. On the basis of thesedeformed algebra, various types of time-evolution of a simple boson system areinvestigated.