  Ordered phases realized through broken continuous symmetries embrace
long-range order-parameter fluctuations as manifest in the power-law decays of
both the transverse and longitudinal correlations, which are similar to those
at the second-order transition point. We calculate the transverse one-loop
correction to the dispersion relation of nonrelativistic Nambu-Goldstone (NG)
bosons at finite temperatures, assuming that they have well-defined dispersion
relations with some integer exponents. It is found that the transverse
correlations make the lifetime of the NG bosons vanish right on the assumed
dispersion curve below three dimensions at finite temperatures. Combined with
the vanishing of the longitudinal "mass", the result indicates that the
correlations generally bring both an intrinsic lifetime to the excitations and
a qualitative change in the dispersion relation at long wavelengths below three
dimensions at finite temperatures, unless it is protected by some conservation
law. A more detailed calculation performed specifically on a single-component
Bose-Einstein condensate reveals that the gapless Bogoliubov mode predicted by
the perturbative treatment is modified substantially after incorporating the
correlations to have (i) an intrinsic lifetime and (ii) a peak shift at long
wavelengths from the linear dispersion relation. Thus, the NG bosons may be
fluctuating intrinsically into and out of the ordered "vacuum" to maintain the
order temporally.
