Method of recurrent construction of Löuwdin spin-adapted wave functions. II. Local representation of creation–annihilation operators

Some compositions of the addition and subtraction operators and recurrence relations for the Sanibel-type coefficients c_{u, v} (n, s, M) generated by these compositions are studied. A local representation of the fermion creation–annihilation operators via the addition and subtraction operators is obtained. Operators of single excitations, coupling, and decoupling operators, in terms of which the unitary group generators can be expressed are defined. The resulting representation of the nonelementary unitary group generators is much more simple than in the Gelfand–Tzetlin basis and in the most general case contains only six logically different terms, each of them possessing quite transparent physical significance.