  We present a theory of the scaling behavior of the thermodynamic, transport
and dynamical properties of a three-dimensional metal at an antiferromagnetic
critical point. We show how the critical spin fluctuations at the AFM
wavevector q=Q induce energy fluctuations at small q, giving rise to a
diverging quasiparticle effective mass over the whole Fermi surface. The
coupling of the fermionic and bosonic degrees of freedom leads to a
self-consistent relation for the effective mass, which has a strong coupling
solution in addition to the well-known weak-coupling, spin-density-wave
solution. We thereby use the recently-introduced concept of critical
quasiparticles, employing a scale-dependent effective mass ratio m*/m and
quasiparticle weight factor Z. As a consequence of the diverging effective mass
the Landau Fermi liquid interaction is found to diverge in all channels except
the critical one, causing important vertex corrections. The ensuing spin
fluctuation spectrum obeys omega/T scaling. Our results are in good agreement
with experimental data on the heavy fermion compounds YbRh2Si2$ and
CeCu(6-x)Au(x) assuming 3D and 2D spin fluctuations, respectively.
