  We studied dielectric properties of a polar nematic phase (NF) sandwiched
between two gold or ITO electrodes, serving as a cell surfaces. In bulk, NF is
expected to exhibit a Goldstone mode (phason), because polarization can
uniformly rotate with no energy cost. However, because the coupling between the
direction of nematic director and polarization is finite, and the confinement,
even in the absence of the aligning surface layer, induces some energy cost for
a reorientation of polarization, the phason dielectric relaxation frequency is
measured in a kHz regime. The phason mode is easily quenched by a bias electric
field, which enables fluctuations in the magnitude of polarization to be
followed in both, the ferronematic and nematic phases. This amplitude (soft)
mode is also influenced by boundary conditions. A theory describing the phase
and amplitude fluctuations in the NF phase shows that the free energy of the
system and, consequently, the dielectric response are dominated by
polarization-related terms with the flexoelectricity being relevant only at a
very weak surface anchoring. Contributions due to the nematic elastic terms are
always negligible. The model relates the observed low frequency mode to the
director fluctuations weakly coupled to polarization fluctuations.
