Boson Bogolyubov Transformation and theSU(1, 1) Group
Haruo Ui
The homogeneous canonical transformation of boson operators is studied from the standpoint of the SU(1, 1) quasi-spin formalism. It is shown that this transformation can be regarded as a rotation in the SU(1, 1) quasi-spin space. This situation is just analogous to the SU(2) quasi-spin formalism of many-fermion problem, in which fermion Bogolyubov transformation can be regarded as a rotation in the SU(2) quasi-spin space. The transformation law of state vectors under this boson Bogolyubov transformation is then written down explicitly in terms of the SU(1, 1) d-functions obtained in the preceding paper. For clarity, we treat the simplest nontrivial example of one-dimensional harmonic oscillator or, equivalently, a system consisting of one kind of bosons. Generalization to many-boson problem and its possible applications to Bose fluid and nuclear structure are briefly discussed.
Progress of Theoretical Physics•Sep 1, 1970•9 citations