  This work is devoted to several translation-invariant models in
non-relativistic quantum field theory (QFT), describing a non-relativistic
quantum particle interacting with a quantized relativistic field of bosons. In
this setting, we aim at the rigorous study of Cherenkov radiation or friction
effects at small disorder, which amounts to the metastability of the embedded
mass shell of the free non-relativistic particle when the coupling to the
quantized field is turned on. Although this problem is naturally approached by
means of Mourre's celebrated commutator method, important regularity issues are
known to be inherent to QFT models and restrict the application of this method.
In this perspective, we introduce a novel non-standard construction procedure
for Mourre conjugate operators, which differs from second quantization and
allows to circumvent regularity issues. To show its versatility, we apply this
construction to the Nelson model with massive bosons, to Fr\"ohlich's polaron
model, and to a quantum friction model with massless bosons introduced by
Bruneau and De Bi\`evre: for each of these examples, we improve on previous
results.
