Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin—the states built from spin and spatial wave functions belonging to multidimensional irreducible representations of the symmetric group, unless the total spin has the maximal allowed value. For spin-dependent one-body interactions with external fields and spin-independent two-body ones between the particles, the sum dependence on the many-body states is given by universal factors, which are independent of the interaction details and Hamiltonians of noninteracting particles. The sum rules are applied to perturbative analysis of energy spectra.

• Received 25 January 2015

DOI:https://doi.org/10.1103/PhysRevA.91.053601