Kartik Prabhu
Tired of slap-fest? Why not read something new about infrared scattering in QFT and quantum gravity: https://arxiv.org/abs/2203.14334
The usual formulation of scattering for massless fields (which escape to null infinity) is beset by divergences in the infrared (IR), i.e, the S-matrix amplitudes diverge at zero frequency. This zero frequency effect is directly related to the physical memory effect; so we cannot just wish this IR divergence away. At null infinity, this memory effect labels an infinite-number of Hilbert spaces all of which are unitarily-inequivalent!
In QED with massive scalars, the Faddeev-Kulish construction by gives a nice way to stitch these Hilbert spaces together, by “dressing” all the in/out massive states with memory to have a fixed value of infinitely-many charges at spatial infinity which is conserved in scattering.
If you use a massless scalar source, the “dressing” becomes too singular — so singular in fact that the energy flux through null infinity diverges! Massless charged scalars do not wear a shirt to the red carpet!
But then GR shows up and slaps all the dressings in the face! The only state in GR which has fixed charges at spatial infinity is the Minkowski vacuum state! Mayhaps GR will win an Oscar someday too…
The issue really is trying to shoehorn all the quantum states into a single Hilbert space; quantum states, in the algebraic sense, are perfectly well-defined. So we suggest that we should try to define scattering also in the algebraic formulation.
Kartik Prabhu
Can someone explain to me what the hell UV/IR mixing means?
Kartik Prabhu
Here is a video from Segal’s talk at IAS
https://www.ias.edu/video/wick-rotation-and-positivity-energy-quantum-field-theory