Generalized Bose Operators in the Fock Space of a Single Bose Operator

Generalized Bose operators b which reduce by two the number of quanta of a Bose operator a are studied in the Fock space of a. All representations of the b's as normal-ordered (infinite degree) power series of the a's are found. The unitary operators relating the irreducible components of b to a are also exhibited. The analogous result for b(k)'s which reduce the number of a quanta by k is given and the limit k → ∞ is discussed.