Characteristic operators and unitarily invariant decomposition of hermitian operators

A set of characteristic operators { F   q p ′ p } is proposed for performing the decomposition of p ‐particle Hermitian operators { D p } to constitute irreducible components { D   q p } of the unitary group D   q p= F   q pp D p , q = 0,1,2,…, p . For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p ‐particle Hermitian operators are obtained as a number of terms having invariant group‐theoretical meaning.