Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

Abstract

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.

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

References in corpus (4)

• Infraparticle Scattering States in Non-Relativistic QED: I. The Bloch-Nordsieck Paradigm
• Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties
• Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
• Lower Spectral Branches of a Spin-Boson Model

Cited by in corpus (3)

• Some Hamiltonian Models of Friction
• The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold
• Quantum Electrodynamics of Atomic Resonances