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##### The BCS-Bogoliubov and the $su(2)$-Algebraic Approach to the Pairing Model in Many-Fermion System

**Authors**: Yasuhiko Tsue, Constança Providência, João da Providência, Masatoshi Yamamura

**Ref.**: Progress of Theoretical Physics **128**, 693-715 (2012)

**Abstract**: The relation between two approaches to the su(2)-algebraic many-fermion model is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the quasiparticles representing all the degrees of freedom except those related to the Cooper-pairs and (2) the conventional algebraic approach in terms of the use of the minimum weight states, from which the Cooper-pairs are excluded. In order to arrive at the goal, the idea of the quasiparticles is brought up in the conservation of the fermion number. Under the c-number replacement for the three su(2)-generators, the quasiparticles suggested in this paper are reduced to those in the BCS-Bogoliubov approach. It is also shown that the two approaches are equivalent through the c-number replacement. Further, a certain modification of the BCS-Bogoliubov approach is discussed.

**DOI**: 10.1143/PTP.128.693