  We present diagrammatic approximations to the spin dynamics of the 2d
Heisenberg antiferromagnet for all temperatures, employing an auxiliary-fermion
representation. The projection onto the physical subspace is effected by
introducing an imaginary-valued chemical potential as proposed by Popov and
Fedotov. The method requires that the fermion number at any lattice site is
strictly conserved. We compare results obtained within a self-consistent
approximation using two different auxiliary-particle projection schemes, (1)
exact and (2) on average. Significant differences between the two are found at
higher temperatures, whereas in the limit of zero temperature (approaching the
magnetically ordered ground state) identical results emerge from (1) and (2),
providing the qualitatively correct dynamical scaling behavior. An
interpretation of these findings is given. We also present in some detail the
derivation of the approximation, which goes far beyond mean-field theory and is
formulated in terms of complex-valued spectral functions of auxiliary fermions.
