Spontaneous photon emission from a non-relativistic free charged particle in collapse models: A case study

• We compute the electromagnetic radiation emission in collapse models.
• Equations of motion are exactly solved under only the dipole approximation.
• The correct emission rate is found treating the electromagnetic interaction exactly.
• The emission rate can be computed using a semiclassical calculation.

We study the photon emission rate of a non-relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic potential. The physical quantity we will be interested in is the spectrum of the radiation emitted by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appearing in the literature, regarding the exact mathematical formula of a spectrum for a free particle.