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The relation between two approaches to the su(2)-algebraic many-fermion modelis discussed: (1) the BCS-Bogoliubov approach in terms of the use of thequasiparticles representing all the degrees of freedom except those related tothe Cooper-pairs and (2) the conventional algebraic approach in terms of theuse of the minimum weight states, from which the Cooper-pairs are excluded. Inorder to arrive at the goal, the idea of the quasiparticles is brought up inthe conservation of the fermion number. Under the c-number replacement for thethree su(2)-generators, the quasiparticles suggested in this paper are reducedto those in the BCS-Bogoliubov approach. It is also shown that the twoapproaches are equivalent through the c-number replacement. Further, a certainmodification of the BCS-Bogoliubov approach is discussed.

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