Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

Details Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

2010-01-05

arxiv.org/abs/1001.0688v4

Annales Henri Poincare 11:1545-1589,2010

Physics

Mathematical Physics

Revised version: a remark added at the end of Section 5

Scientific paper

10.1007/s00023-010-0066-z

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.

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