Field-theory renormalization and critical dynamics above $T_c$: Helium, antiferromagnets, and liquid-gas systems

The Martin-Siggia-Rose field theories associated with the critical dynamics of mode-coupling systems, are renormalized in a way which decouples statics from dynamics, through the minimal-renormalization procedure. This simplifies considerably the computations which are thus carried out to two-loop order for exponent and Wilson functions. We obtain all dynamic transients for helium, $O\left(n\right)\mathrm{}$ symmetric antiferromagnets, and liquid-gas systems. We also discuss the relevance for helium of a fixed point where dynamic scaling is weakly violated.