This evening, I was lucky enough to dine with Brenda Penante, Stephane Launois, Lionel Mason, Nima Arkani-Hamed, Tom Lenagan and David Hernandez. Here for your delectation are some tidbits from the conversation.

- The power of the renormalisation group comes from the fact that the $1$-loop leading logarithm suffices to fix the leading logarithm at all loops. Here’s a reference.
- The BPHZ renormalisation scheme (widely seen in the physics community as superseded by the Wilsonian renormalisation group) has a fascinating Hopf algebra structure.
- The central irony of QFT is thus. IR divergences were discovered before UV divergences and “solved” almost instantly. Theorists then wrangled for a couple of decades over the UV divergences, before finally Wilson laid their qualms to rest. At this point the experimentalists came back and told them that it was the IR divergences that were the real problem again. (This remains true today, hence the motivation behind my work on soft theorems).
- IR divergences are a consequence of the Lorentzian signature. In Euclidean spacetime you have a clean separation of scales, but not so in our world. (Struggling to find a reference for this, anybody know of one?)
- The next big circular collider will probably have a circumference of 100km, reach energies 7 times that of the LHC and cost at least £20 billion.
- The Fourier transform of any polynomial in with roots at for has all positive coefficients. This is equivalent to the no-ghost theorem in string theory, proved by Peter Goddard, and seems to require some highly non-trivial machinery. (Again, does anyone have a reference?)

and finally

- Never, ever try to copy algebra into Mathematica late at night!

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“IR divergences are a consequence of the Lorentzian signature.”

Could you maybe elaborate a little more? I was taught that they stem from massless particles in the theory. In particular, on also needs to regularize the QFTs used in Condensed Matter in the IR once you have massless excitations.

Or is your point that there the usual ways to deal with it pose no problem as there is a “clean separation of scales”?