@qwerty oh yes I think so. Might have been from Collier's videos. But his style of flaunting privilege is just so common...

@imbAF it depends what you mean. the conventional notion of SSB (to my understanding) is when a system with Hamiltonian $H$ with symmetry group $G$ is found in a stable state $\Psi$ that is not invariant under all of $G$. this is formally understood to only be possible in the thermodynamic limit. to my understanding it's not well understood what various mechanisms actually cause SSB to happen in the sense of what causes a system to choose one stable state over another.

@SillyGoose You're talking to someone trying to learn hep-th/relativistic QFT. There is no "thermodynamic limit" in that case.

@naturallyInconsistent aliens~

Also, you don't need a "mechanism" to choose one state "over another" in this "thermodynamic limit" because in most versions of the Higgs mechanism some combination of gauge invariance and superselection rules will mean you can't distinguish the different vacua anyway

And again, as I already said above, SSB is not something that "happens" in zero-temperature hep-th QFT. The theory does not go from unbroken to broken, it's just always broken. Situations where you have actual phase transitions (in the sense that something actually "happens" at some point in time) occur only if you do QFT at finite temperature or some other version where the ground state can be dynamic.

The closest to the "thermodynamic limit" would be if you conceive of a QFT primarily as being defined by a lattice theory in a box and then take the limit of infinite box volume and infinitely small lattice spacing - it's folklore that only in this limit, SSB "can happen". The mathematical interpretation of this is yet again Haag's theorem allowing inequivalent irreps of the field operators, each "above a different SSB vacuum". But since they are irreps, they form superselection sectors.

From a more physical viewpoint, Weinberg (the second volume) has a discussion of how only certain combinations of the vacua (precisely the "superselected ones") obey cluster decomposition.

what exactly are some issues with defining QFT from lattice models?

@SillyGoose you can't prove the continuum limit exists

at least not generically

famously the continuum limit of $\phi^4$ lattice theory is "trivial", i.e. free but at a physical level of rigor we don't believe $\phi^4$ continuum theory is free

also there's loads of issues with Lorentz invariance, fermion doubling, etc.

@qwerty oooOOOooo~

well, in reality, the whole topic is more complicated than "trivial" = "free" in that this mostly affects some "infrared scaling" properties but there's a lot of subtlety here where if you think QFT is defined by the lattice theory this isn't so worrisome but if you think about QFT as a continuous theory approximated by the lattice theories it's more concernin

hm for some reason i am partial to thinking the world should be more like a lattice in reality than a continuum

I don't really want to claim I understand every aspect of this but I want to caution against conflating a) lattice QFT b) non-relativistic continuous QFT c) relativistic continuous QFT - they are all interrelated, but at varying levels of rigor and if you just talk about "QFT" it's very easy to end up with inconsistent statements

@SillyGoose I'm partial to thinking the opposite. Now what :P

@ACuriousMind now we dual

@SillyGoose so I'm co-silly goose and you're CoCuriousMind?

not sure how that resolves the issue :P

maybe our duals map us into an easier problem :P

i think i'll take a break from QFT land...on to renormalization group~

...how is renormalization not about QFT :P

well i am reading about it with a statistical mechanics emphasis

that's just QFT with extra steps ;)

hit them with the wick rotation \ ~_~ /

also i saw a book by one of our very own today at my uni's library

er edited by one of our very own

@SillyGoose you joke but Wick rotation is one of those things where I cycle between "it actually makes sense" to "this makes no sense at all" with alarming frequency :P

the mathematical physics buzzword is Osterwalder-Schrader reconstruction

i need to make a list of mathematical physics buzzwords

@SillyGoose Cosmas frequently links his papers and books, he's not particularly shy about being a big proponent of the phase space formulation :P

there are some really nice bits in phase space formulation

it's pretty neat until you actually have to compute a Moyal bracket :P

@ACuriousMind most of the time its invocation is not trying to do any rotation at all, but rather are analytical continuation so that contour deformation can be used to cast the offending integral into an easier-to-evaluate equivalent. In some rare cases it is actually going deeper into stationary phase steepest descent method, which is also the proper way to do Fresnel integrals.

@ACuriousMind but we obviously rarely do that. Like, there are plenty of stuff in physics and maths whereby some stuff are nice to look at, but cumbersome to stick strictly with.

path integral be like

@naturallyInconsistent I know, the formal statement of the OS theorems is about the analytic continuation of Euclidean correlation functions to Minkowski correlation functions. But it is the only meaningful formalization of the "Wick rotation" idea.

The entirety of the constructive path integral approach to QFTs a la Glimm and Jaffe is based on this idea.

the combinatorial way is always the most intuitive to attempt to set up but is hopeless to really compute unless you want to contemplate counting for a long while...

i picked up a book by glimm and jaffe on statistical mechanics today hehe

didn't know they had such a text

okay i guess it's on QFT and SM

@SillyGoose In their modesty they simply called it "Quantum Physics - A Functional Integral Point of View"

oh i mean this book link.springer.com/book/10.1007/978-1-4612-5158-3

@ACuriousMind I really think this ordering is awkward. What we really want are the Minkowski versions. But I suppose in a rigorous mathematical treatment they indeed do have to present the Euclidean version first.

@naturallyInconsistent The very heuristic point is that proving convergence of the Euclidean integrals is easier because proving convergence of integrals over $\mathrm{e}^{-S}$ is easier than proving integrals over $\mathrm{e}^{\mathrm{i}S}$ even exist

So once you have the OS theorems the "only" task is proving those integrals exist. Unfortunately I'm not aware of any major progress since Glimm and Jaffe, i.e. we know this programme works for a lot of 2d and 3d theories but 4d Standard-Model-like theories are still intractable

Yes, you've told meow meow that the only treatment of QFT relevant to hoomanity that works is the Causal Perturbation stuff.

I'm not sure that's my position. Causal Perturbation Theory offers a way to construct the S-matrix perturbatively without having ill-defined infinite quantities in intermediate steps, but that's not really what the kind of QFT I'm talking about above is about

anything I've talked about above is not perturbative

Oh, thanks~

a person named RG Priest writing a paper about RG lol: journals.aps.org/prb/abstract/10.1103/PhysRevB.11.3461

morning

@ACuriousMind not sure, plenty of stuff is true but I can't prove it :P

@qwerty it can't be Friday

Oh, it's Friday

that's the feeling I get when I realise we're halfway through the decade :p

We're not halfw-

Oh come on, qwerty

Can you believe that 2050 is closer than 2000?! I'm closer to being a 50yo than my birth

Quarter age crisis

in our defence, I think there was a period of really rapid technological and cultural change between say 1955 to 1990, versus 1990 to 2025. (but that doesn't help with my personal crisis of "help I'll never learn and really understand all the physics I want let alone contribute anything meaningful before I die" :P)

I'm over that phase, I'm just looking for ways to get money and get a lot of spare time :P

There are many brilliant minds that contribute and will contribute to physics, so I can be selfish and never give my average person contribution, only doing physics when I feel like it

@SignorFeynman ... and use that spare time to do physics? :*suspicious*:

@SignorFeynman hehe yeah

I'm also closer to being a 50yo than my birth. Except I'm on the other side of 50. :D

Unless I set a new record for longevity I'm nearer death than birth, which is a sobering thought :-)

I'm slightly older than you, John: I was born in 1959.

this conversation calls for some monty python youtube.com/watch?v=SJUhlRoBL8M

@PM2Ring parity symmetry

@qwerty I expected you to link to "Four Yorkshiremen". Here's the original version, before Monty Python, with Tim Brooke-Taylor, John Cleese, Graham Chapman and Marty Feldman.

@fqq I foresaw that objection, which is why I added "or point to a proof in the literature" :P

@ACuriousMind Any idea about this

@Slereah nope

you have plunged into depths/climbed to heights of category theory where I dare not tread

lol

Alas

Getting a lot of that asking around :p

XGW was trained in string theory...so now can i use pursuing CMT as an excuse to study string theory ;)

When category theorists get confused, they ask Slereah to point out a ref

is the spin-blocked 1D Ising model a genuine example of renormalization group?

or is it like a toy half-on-the-mark example

As far as I can tell, the sharp modality gives you the trivial topology while its negation gives you the infinitesimal structure around a point, the flat modality gives you the trivial topology while the negation is some one-point space with the same local properties as all other points, and the shape modality gives you the fundamental groups while its negation gives you the universal cover at a point

when category theorists get confused they draw another arrow

i am a little bit confused what a renormalization group physically corresponds to

in the Ising model, as we iteratively course-grain, we flow into a coupling constant which corresponds to a high temperature version of the same Ising model

@SillyGoose well, there is the whole duality thing in CFT/AdS stuff (I only know the buzz words plus some extreme basic ideas)

oh hm

so like you generate your nice little critical point CFT and then perhaps it has a dual gravitational theory?

I have no idea (as I said) haha

also your remarks from our previous conversation were helpful (about the vacuum business)

glad I could help a bit

another thing i don't get: seemingly RG should leave the partition function invariant as presented in spin-blocking an Ising model

because you are just explicitly performing part of the sum that computes the partition function exactly over some of the spins

okay i guess it's supposed to

@SillyGoose The partition function basically encapsulates all the average values i.e. physical quantities, that you want to be invariant under a non-physical transformation such as the RG action

@SillyGoose yes, this is the mathematical reason

@SillyGoose There was some hype regarding AdS/CFT in relation to strange metals IIRC

However most CM theorists don't really do any of this stuff

does anyone know where the $\frac{1}{3}$ factor comes from in (3.11)?

If you want a crazy hard CMT book, there is "Bosonization and Strongly Correlated systems"

seemingly its origin should be that we are blocking our 1D Ising chain into blocks of three spins

(3.6) is describing a typical interaction term between two blocks, for example between spins $3,4,5,6$: | 2 3 4 | 5 6 7 |

@PM2Ring Looks okay, including a little bit of Chernobyl

What was that? A soil sample? It looks like one.

And the age of the sample doesn't mean much. Depending on the weather, there may be significant activity of new Be-7 in ground-level air and on surfaces.

@Loong He didn't say. All he posted was the stuff I quoted above, and this comment:

okay

Which was originally posted as an answer, but Qmechanic converted it to a comment.

If he is using that reference, he should be fine. At least concerning the natural background in his sample.

Why does the K-40 have such high activity?

Maybe it's a soil sample. Or the ash of a plant sample.

Ah, right.

The actinium & caesium are from Chernobyl?

The Cs-137 is from Chernobyl.

With that Cs-137/K-40 ratio, it looks like a soil sample from Europe.

depending on the detector efficiency curve

The Ac-228 is from the natural Th-232 chain.

Ok.

Peter has been a member for only 4 days?

@skullpatrol Yes. Hence his low rep. I guess he tried to do the right thing by adding to an existing "thread", not realising that Stack Exchange isn't a forum...

Right.

This raises the Chernobyl TV mini-series on my list of things to watch.

It's not completely bad, but it allows itself a lot of artistic liberties. The presented science and nuclear technology have to be taken with a grain of salt.

Would you re-watch it?

I have to say, I enjoyed watching it, but mostly because of the dramaturgy.

And I always liked Stellan Skarsgård.

But a few unnecessary factual mistakes can get you upset.

The Netflix series about Fukushima is closer to the reality.

You don't learn much about reactor accidents, but a lot about cultural differences.

okay, thanks for the suggestions

@ACuriousMind Ahh. This makes a lot of sense now.

@Sanjana hey!

hi

Even the podcast associated to the show is good

thanks for sharing