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

TL;DR

This paper introduces a novel boson representation of the su(2)-algebra based on the su(1,1)-algebra, offering new tools for modeling time-dependent quantum systems interacting with environments.

Contribution

It presents a new boson representation of su(2) derived from su(1,1), contrasting with the Schwinger representation, and explores related algebra deformations and their applications.

Findings

New boson representation of su(2) proposed

Application to time-dependent quantum systems

Analysis of algebra deformations and dynamics

Abstract

With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra which is also based on two kinds of bosons. This representation may be suitable for describing time-dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., the phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebra, various types of time-evolution of a simple boson system are investigated.