A possible boson realization of the so(4)- and the so(3, 1)-algebra. In relation to the Runge-Lenz-Pauli vector

As natural extensions of the boson realizations of the su(2)- and su(1, 1)-algebras, the so(4)- and so(3, 1)-algebras are presented in the form of boson realizations with four kinds of boson operators. For each algebra, two forms are discussed. One is constructed in terms of two sets of the boson operators which play the role of spherical terms of rank 1/2. The other is based on the ranks 1 and 0. As a possible application, the Runge-Lenge-Pauli vector, which is famous in the in the context of the hydrogen atom, is derived with some aspects. (author)