IR divergences and total energies....

[asimov42]

I've done some recent reading on IR divergences (propagators becoming singular, etc.). I believe I understand collinear divergences (to some extent)... but I'm not sure about total energies for (primarily) soft photons.

In all scattering experiments, total energy should be conserved - but if all interactions are generating soft photons, and those soft photons are then participating in other interactions, and this goes on ad infinitum - do we also end up with divergence in energy (over a finite spatial volume)? This energy would have to already have been present (and I'm focusing on photons only) in the em field.

Essentially, I'm wondering about the exact nature of the divergences ... why everything isn't 'floating' in an infinite sea of soft photons.

Apologies for the poor statement of the question - I'm happy to try to clarify.

 

[mfb]

why everything isn't 'floating' in an infinite sea of soft photons.

We are, sort of. We have electromagnetic fields everywhere. The total energy density in the field is finite.

 

[PeterDonis]

f all interactions are generating soft photons, and those soft photons are then participating in other interactions, and this goes on ad infinitum - do we also end up with divergence in energy (over a finite spatial volume)?

No, because soft photons can have arbitrarily low energy per photon. In the limit, heuristically, you can have an infinite number of photons each with zero energy, which adds up to zero (or at least negligible) energy.