  We demonstrate that the `microscopic' field theory representation, directly
derived from the corresponding master equation, fails to adequately capture the
continuous nonequilibrium phase transition of the Pair Contact Process with
Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not
allow for a stable fixed point in the parameter region that is accessible by
the physical initial conditions. There exists a stable RG fixed point outside
this regime, but the resulting scaling exponents, in conjunction with the
predicted particle anticorrelations at the critical point, would be in
contradiction with the positivity of the equal-time mean-square particle number
fluctuations. We conclude that a more coarse-grained effective field theory
approach is required to elucidate the critical properties of the PCPD.
