Causal quantum-mechanical localization observables in lattices of real projections Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal project...

did you see this? I DMed you a recorded talk by Lechner about this at one point also. It's super interesting imo

happy birthday!!

(surely Understanding QFT was never a binary in the first place)

right but there you've used + in the LHS. The point of the paper is that you get it (and more) from iterated application of EML(x,y) no?

I don't think you can get x+y from just your f though?

I dimly recall a headline that this used to be a thing, i.e. telling the LLM it would get paid slightly improved results or something some years ago. But with the amount of post-training separating models from next-token-prediction these days idk if that's still true

anyone want to be my friend in some dark way?

en.wikipedia.org/wiki/Wikiped...

The fact that the amplitudes going into this correlation are complex instead of real means they can cancel against each other, which seems catastrophic—probability no longer monotone!—but works out and is basically just true in the real world

The fields need to be smeared a bit for the squares in the denominator to be well-defined, but this is already true for classical random fields. The smearing has physical relevance determined by what our detectors actually measure, like a point-spread function of a camera.

one thing you can observe in the way of statistics is the norm-square, <φ(y)φ(x)><φ(x)φ(y)>/(<φ(x)²><φ(y)²>). The usual interpretation is 'the probability for a particle prepared at x to be found at y', but without talking about particles compare it to classical R²=Cov(X,Y)²/(Var(X)Var(Y))

it's like a trap for me personally

we love to see a book whose toc has
- QM interpretation which includes coarse-graining
- Morse theory
- BV/BRST but also "gauge theory w/o ghosts"
- "X22: Quantum mechanics on a Klein bottle"
on top of a comprehensive & opinionated exposition of QFT?

what the hell this book looks great I never knew

Does Coleman-Mandula put any restriction or pressure on classical field theories?

at least we can still interpret it as a transition amplitude 😌

no this particular thing is just a UV divergence that's independent of quantization imo. As in, for a Gaussian free field as probabilists consider, φ(x)² aready does not make much sense as a RV. It's not so bad in 1d (ordinary Brownian motion), which corresponds to 0+1d QFT, i.e. QM

the paper by Geroch which he cites has the same limit λ→0 but doesn't call it 'shrinking the mass' which just seems confused?
though I agree that counterfactuals like this are difficult in GR, but am not sure whether more so than in other gauge theories

as everyone knows from kindergarten,

The existence of reginos implies the existence of their supersymmetric partners: regions

windshields used to have squashed bugs

I too would be happy if I were a boson

once you end one, you can't help but end another. It's like heroin

I guess this is the neuro version of 'the lines are particles' ^^

Don't feel to bad. I, for one, am equally washed

qft has been reimagined so many times. The problem is not that all approaches are founded in folklore, it's just that it's hard to see the whole elephant

@gro-tsen.bsky.social possible inspiration here for your website?

nice. I think another (definitely algebraic) example can be made from the total space of a vector bundle, e.g. a deg-0 line bundle on a curve which is not a torsion point of the Jacobian

I suspect there might be some difficulty in reaching him

If the metric change is caused locally surely there is no problem. i.e. given a solution of gr with matter, if I change the flow of the matter in some local region, the ensuing solution is unchanged outside of the perturbation's future, right? (but idt creating a grav wave in a vacuum is a local op)

tbh I think christians should invent cool sanitized uwu smol bean versions of christian belief if it helps them get with the times lol