Absence of ground states at large total momentum in translation-invariant polaron models

Determine whether, for translation-invariant polaron models at fixed total momentum P (including the Fröhlich polaron and the Bose polaron without ultraviolet regularization), ground states are absent at sufficiently large |P|, thereby proving the conjectured nonexistence of ground states in that regime.

Background

The authors situate their results within non-relativistic quantum field theory and discuss analogous phase-transition phenomena in polaron models. For fixed total momentum, ground states at small |P| are known to exist, but the expected absence at large |P| remains mostly unproven.

They highlight that only in the ultraviolet-regularized Fröhlich polaron has absence at large momentum been established, leaving a broader open question in the field.