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As natural extensions of the boson realizations of the su(2)- and thesu(1,1)-algebra, the so(4)- and the so(3,1)-algebras are presented in the formof boson realizations with four kinds of boson operators. For each algebra, twoforms are discussed. One is constructed in terms of two sets of the bosonoperators which play a role of spherical tensor with rank 1/2. The other isbased on the ranks 1 and 0. As a possible application, the Runge-Lenz-Paulivector, which is famous in the hydrogen atom, is derived with some aspects.Comment: 22 pages, no figur

A Possible Boson Realization of the so(4)- and the so(3,1)-Algebra: -- In Relation to the Runge-Lenz-Pauli Vector --