On the spontaneous emission of electromagnetic radiation in the CSL model

• We compute the electromagnetic radiation emission in collapse models.
• Under only the dipole approximation, the equations of motion are solved exactly.
• The electromagnetic interaction must be treated exactly.
• In order to obtain the correct emission rate the particle must be bounded.

Spontaneous photon emission in the Continuous Spontaneous Localization (CSL) model is studied one more time. In the CSL model each particle interacts with a noise field that induces the collapse of its wave function. As a consequence of this interaction, when the particle is electrically charged, it radiates. As discussed in Adler (2013) the formula for the emission rate, to first perturbative order, contains two terms: one is proportional to the Fourier component of the noise field at the same frequency as that of the emitted photon and one is proportional to the zero Fourier component of the noise field. As discussed in previous works, this second term seems unphysical. In Adler (2013) it was shown that the unphysical term disappears when the noise is confined to a bounded region and the final particle’s state is a wave packet. Here we investigate the origin of this unphysical term and why it vanishes according to the previous prescription. We will see that perturbation theory is formally not valid in the large time limit since the effect of the noise accumulates continuously in time. Therefore either one performs an exact calculation (or at least in some way includes higher order terms) as we do here, or one finds a way to make a perturbative calculation meaningful, e.g., by confining the system as in Adler (2013).