Annales Henri Poincaré

, Volume 11, Issue 8, pp 1545-1589

First online:

Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

  • Wojciech De RoeckAffiliated withInstitut für Theoretische Physik, Universität Heidelberg Email author 
  • , Jürg FröhlichAffiliated withInstitute of Theoretical Physics, ETH Zürich
  • , Alessandro PizzoAffiliated withDepartment of Mathematics, University of California Davis


We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling constant is sufficiently small. More precisely, under the assumption that the fiber eigenvectors corresponding to the putative mass shell are differentiable as functions of the total momentum of the system, we show that a mass shell could exist only at a strictly positive distance from the unperturbed embedded mass shell near the boundary of the energy–momentum spectrum.