  We study the effect of dissipation on quantum phase fluctuations in d-wave
superconductors. Dissipation, arising from a nonzero low frequency optical
conductivity which has been measured in experiments below $T_c$, has two
effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction
of the temperature at which one crosses over to classical thermal fluctuations.
For parameter values relevant to the cuprates, we show that the crossover
temperature is still too large for classical phase fluctuations to play a
significant role at low temperature. Quasiparticles are thus crucial in
determining the linear temperature dependence of the in-plane superfluid
stiffness. Thermal phase fluctuations become important at higher temperatures
and play a role near $T_c$.
