Abstract This work is devoted to several translation-invariant models in nonrelativistic quantum field theory (QFT), describing a nonrelativistic 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 bare nonrelativistic 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 the method. In this perspective, we introduce a novel non-standard procedure to construct Mourre conjugate operators, which differs from second quantization and allows to circumvent many regularity issues. To show its versatility, we apply this construction to the Nelson model with massive bosons, to Fröhlich’s polaron model, and to a quantum friction model with massless bosons introduced by Bruneau and De Bièvre: for each of those examples, we improve on previous results.
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