  We investigate the dynamic response of population transfer between two
components of a finite temperature spinor Bose condensed gas to a
time-dependent coupling potential. Comparison between results obtained in the
Bogoliubov-Popov approximation (BPA) and in the generalized random phase
approximation (GRPA) shows noticeable discrepancies. In particular, the
inter-component current response function calculated in the GRPA displays a
gapped spectrum due to the exchange interaction energy whereas the
corresponding density response function is gapless. We argue that the GRPA is
superior since, contrary to the BPA, it preserves the SU(2) symmetry and the
f-sum rule associated to the spinor gas. In order to validate the
approximation, we propose an experimental setup that allows the observation of
the predicted gap.
