The h Bar

qwerty

00:01

ah, the good sort of problem, then?

DIRAC1930

Well I'm running out of time so no lol

Signor Feynman

@qwerty I googled and found that the average surface area of a human being is $1.9\mathrm{m}^2$

Actually, that's for an adult man

But why are you so interested in that piece of information? 🤔

qwerty

lmao

Allie

hm, so a 2mx1m rug's worth

Signor Feynman

So it wouldn't be expensive to buy tiles to cover myself

DIRAC1930

00:04

I think I hate most areas of physics now lol

ACuriousMind

@SignorFeynman You're missing the surface area of the lungs, etc. there. Since we can't close our nostrils, they're topologically outside, too!

Signor Feynman

That PhD is turning you into a villain

qwerty

you're so random signore xD

Signor Feynman

@ACuriousMind I'm assuming a man is just the outer shell! I'm not getting tiles on my lungs!

@qwerty I'm a good clown

qwerty

@SignorFeynman ok Pennywise

ACuriousMind

00:06

@SignorFeynman ...why are you getting tiles for the rest?

Silly Goose

@DIRAC1930 what is the general topic that you are studying?

DIRAC1930

I'd rather not say for anonymity lol

Silly Goose

oh i see

Signor Feynman

For example, today at lunch some people seemed quite sad while discussing with the others, so I put a walnut on the table and cracked it opened it with a heabutt. It fixed the mood :P

ACuriousMind

I choose to believe you always carry a walnut with you for that purpose

qwerty

00:09

hahaha

Signor Feynman

Italian Sunday lunch. Nuts are the last stage before sweets

ACuriousMind

look at signor fancypants, his lunch has stages

Signor Feynman

Probably I should edit to walnuts and hazelnuts. It seems weird like that

qwerty

and after that you must have coffee?

Signor Feynman

Yes and after that amaro

ACuriousMind

00:11

@SignorFeynman I don't think it's the type of nut that makes this weird :P

qwerty

xD

Signor Feynman

I guess I have my mind in the gutter

qwerty

once I got obsessed with amaretti and ate so many that years later i still feel a bit sick of them

Signor Feynman

And it's late enough that I have no filters

Beware that amaro is liquor, amaretti are biscuits

ACuriousMind

I'll give you this: all versions of this event that I can imagine are hilarious, that would at least temporarily distract me from being sad too :P

Signor Feynman

00:14

But my favorite amaro is Disaronno which is made of amaretti

qwerty

@SignorFeynman but they are flavoured with the amaro, right

?

ACuriousMind

I only know amaretto (it's a popular addition to mulled wine in the winter)

qwerty

oh noooo they're not D:

Signor Feynman

Mhhhh I think that the biscuits are independent and Disaronno happens to be made out of them (actually, I'm reading that it's a precise variety sharing the same name)

@ACuriousMind beware that amaretto can be both the liquor (aka amaro) or the biscuit

ACuriousMind

@SignorFeynman I mean liquor, but I'm a bit confused because at least the German and English Wikipedia seem to think "amaro" and "amaretto" are different kinds of liquors, now you say "aka amaro" as if they're the same?

DIRAC1930

00:18

As I got older, the less I prefer research, and the more I just want to learn wrong theories from the 1930s

ACuriousMind

perhaps an inside Italy/outside Italy difference?

qwerty

I've had this before also added to mulled wine / hot chocolate en.m.wikipedia.org/wiki/Amaretto

I was confused and thought the biscuit flavour came from that but it seems it's independent

Allie

hi meow

Signor Feynman

@ACuriousMind either amaretto is a subcategory or I'm unreliable :P

Allie

"The energy of an atom in an ideal monatomic gas can be written as the sum of its translational energy and its electronic energy: $\varepsilon_{\mathrm{atomic}} = \varepsilon_{\mathrm{trans}} +\varepsilon_{\mathrm{elec}} $

is this statement a form of the BO approximation?

ACuriousMind

00:28

@SignorFeynman "Amaretto is distinct from amaro, a type of bitter Italian liqueur made from herbs, roots, flowers, bark, and/or citrus peels" - I had never heard of amaro, but that page describes what I mean by amaretto

@Allie Isn't Born-Oppenheimer that you can separate the wavefunction into the product of nuclear and electronic wavefunctions? I don't think the statement about the energy is approximative at all, it's just a fact that you have a term in the Hamiltonian that describes the motion of the atom and a term that describes the electrons' binding to the atom.

Allie

yes, thats the form of the BO approximation that I usually deal with (in DFT). the form im talking about is something i ran into during my pchem class last semester

and I had the exact same question as you

Born–Oppenheimer approximation

In quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the best-known mathematical approximation in molecular dynamics. Specifically, it is the assumption that the wave functions of atomic nuclei and electrons in a molecule can be treated separately, based on the fact that the nuclei are much heavier than the electrons. Due to the larger relative mass of a nucleus compared to an electron, the coordinates of the nuclei in a system are approximated as fixed, while the coordinates of the electrons are dynamic. The approach is named after Max Born and his 23-year-old...

read under "in molecular spectroscopy"

ACuriousMind

ahh, it's a statement about energies, i.e. eigenvalues of the Hamiltonian, not the Hamiltonian itself

so the approximation is that you're in a state that's a simultaneous eigenstate of those parts of the Hamiltonian

I can buy that that's equivalent or at least sufficiently close to the assumption about the state being separable

Allie

yeah

in my case they're doing it so they can separate the partition function into translational and electronic partition functions

Silly Goose

01:08

is wilsonian RG mathematically rigorous?

PM 2Ring

04:30

@qwerty It's not a good idea to consume apricot kernels in large quantity, due to the risk of cyanide poisoning. en.wikipedia.org/wiki/Amaretto & en.wikipedia.org/wiki/Amygdalin

Apricot kernel

An apricot kernel is the apricot seed located within the fruit endocarp, which forms a hard shell around the seed called the pyrena (stone or pit). The kernel contains amygdalin, a poisonous compound, in concentrations that vary between cultivars. Together with the related synthetic compound laetrile, amygdalin has been marketed as an alternative cancer treatment. However, studies have found the compounds to be ineffective for treating cancer. == Use == The kernel is an economically significant byproduct of fruit processing and the extracted oil and resulting press cake have value. Apricot kernel...

Mind you, humans have been consuming foods with cyanide for thousands of years. Fortunately, dangerous cyanide compounds tend to be water-soluble, so it's possible to reduce the cyanide concentration by proper preparation.

Cassava

Manihot esculenta, commonly called cassava, manioc, or yuca (among numerous regional names), is a woody shrub of the spurge family, Euphorbiaceae, native to South America, from Brazil, Paraguay and parts of the Andes. Although a perennial plant, cassava is extensively cultivated in tropical and subtropical regions as an annual crop for its edible starchy tuberous root. Cassava is predominantly consumed in boiled form, but substantial quantities are processed to extract cassava starch, called tapioca, which is used for food, animal feed, and industrial purposes. The Brazilian farofa, and the related...

qwerty

@PM2Ring oh yeah I've heard this about apple seeds

britannica.com/story/can-apple-seeds-kill-you

Britannica claims between 150 to several thousand crushed seeds, which is... hmmm several orders of magnitude

I didn't know cassava contained cyanide!

naturallyInconsistent

04:50

I heard cassava is dangerous if prepared badly. Maybe because of that.

@ACuriousMind It is actually necessarily approximative (in principle, though not very much practical to try to do without) because, as you definitely know, the electron wavefunction is necessarily infinitely large and thus will overlap other atom's electrons if you have more than one nucleus in the universe under consideration. This is, of course, not very important until like in condensed matter, the atoms are close enough that bonding can happen.

@TobiasFünke with only minor alterations in the wordings: In principle, you can aim to talk to everybody and help everybody, but there are practical limitations...

PM 2Ring

> Societies that traditionally eat cassava generally understand that processing (soaking, cooking, fermentation, etc.) is necessary to avoid getting sick. Brief soaking (four hours) of cassava is not sufficient, but soaking for 18–24 hours can remove up to half the level of cyanide.

There is some concern that food shortages associated with climate change may increase cassava-related food poisoning.

naturallyInconsistent

05:06

That's horrifying.

PM 2Ring

Extracting Cyanide From Apple Seeds With Hydraulic Press

►

qwerty

> Industrial production of cassava flour, even at the cottage level, may generate enough cyanide and cyanogenic glycosides in the effluents to have a severe environmental impact.

o.O

PM 2Ring

It's pretty scary that cassava is a major food source for some of the most densely populated regions on the planet.

qwerty

I do often buy cassava chips from my local Indonesian grocer. maybe time to read more about it

PM 2Ring

They should be safe. It's pretty easy to test for cyanide. And any food manufacturer using modern methods ought to be testing their product properly...

Some people eat even more toxic stuff. Eg, I heard there's a delicious variety of potato in South America that has a very toxic alkaloid. You have to grate it, then rinse it in running water for a few days to flush the alkaloid out.

qwerty

05:18

oh I meant the environmental impacts... not that one person will make any difference...

PM 2Ring

I occasionally wonder how people discovered there was a safe way to eat these things...

@qwerty Ah. Well, you can break down the cyanide by oxidisation, and/or heat. But of course that adds to the manufacturing cost...

qwerty

@PM2Ring here's a snarky reddit thread on the topic reddit.com/r/AskAnthropology/comments/davacr/…

PM 2Ring

So modern factories should be able to manage their cyanide waste. But there's a lot of cottage-level production going on that just dumps the cyanide into the environment.

@qwerty Thanks

qwerty

05:45

have you ever tried a gros michel banana @PM2Ring ?

naturallyInconsistent

Given his age, most likely~

PM 2Ring

@qwerty I think so. When I was very young, my grandparents had some banana trees (in Sydney). I'm pretty sure they were Gros Michel.

Most modern bananas aren't as tasty as the ones I had as a kid. But that's not just because of the cultivar. Most modern bananas are picked green & ripened artificially. That was just starting to happen when I was a kid. Fruit & vegies were much more seasonal back then.

qwerty

oh I saw some banana trees in a back alley around the inner west a couple of years ago. I didn't think we had the climate for bananas

@PM2Ring mhmm that makes a lot of sense. people say this a lot about tomatoes in particular

also red delicious apples

PM 2Ring

Sydney is a bit cool for bananas. But you can do tricks, like putting a plastic bag over the banana bunch to create a mini greenhouse.

I lived outside Coffs Harbour from 2010-2017. Banana production in the region has decreased, but they're still plentiful & cheap. But mostly just modern cultivars.

qwerty

big banana!!

PM 2Ring

05:59

@qwerty Definitely. Most large tomatoes these days are pretty tasteless The small ones aren't too bad.

qwerty

@PM2Ring there's no pineapples near the big pineapple anymore :(

PM 2Ring

Tomato cultivars were selected to be able to survive transportation. Tasty ones tend to be squishier. When these new cultivars started appearing in the mid-70s, my grandpa called them "bullet-proof tomatoes".

naturallyInconsistent

bb gun bullets?

PM 2Ring

Blueberries now dominate the Coffs region, not bananas. I guess that's better for the environment, though. 20th century banana cultivation used some pretty heavy chemicals to stop pests & fungus...

qwerty

I suppose it tracks with food trends. it's funny to think of foods being in and out of style... but it seems to be a phenomenon

naturallyInconsistent

06:06

food fashion

as long as it is not food fascist

PM 2Ring

:67246483 The blueberry farms do employ a lot of seasonal workers. But I don't know what proportion are immigrants. There are lots of young back-packers, but some of them are from Australia.

The banana industry certainly relied on a lot of immigrant workers, especially from India. There's a huge Indian community in Woolgoolga: I was told that a few Indian villages essentially transplanted themselves to the region.

Woolgoolga, New South Wales

Woolgoolga is a town on the Mid North Coast of New South Wales, Australia. It is on the Pacific Highway, approximately 550 km north of Sydney and 365 km south of Brisbane. The closest city to Woolgoolga is Coffs Harbour, which lies 24.8 km to the south. Woolgoolga has two beaches on the Pacific Ocean. The area has long been a centre of banana growing in New South Wales, but this industry has declined in the face of competition from Queensland. Recent times have seen many banana plantations replaced by blueberries after banana sales slumped in the late 1990s. == Demographics == Woolgoolga had a...

qwerty

@PM2Ring I think this or some other communities were featured on an ABC show recently-ish. very heartwarming

PM 2Ring

Woolgoolga is a great place. Very laid back, with excellent restaurants. It can be a bit surreal talking to little kids with strong Punjabi accents. ;) If you're in the area in early spring you have to check out the Curryfest.

Kangaroos hop around the streets, and hang out on the football field and the golf course.

From caravanparkphotos.com.au/woolgoolga_golf_course/target11.html

qwerty

06:28

@PM2Ring sounds amazing, I've made a mental note :)

naturallyInconsistent

07:42

@PM2Ring omg with so many, miao miao iz afraid of being stampeded to death

PM 2Ring

07:57

@naturallyInconsistent Those roos are pretty tame, since they live so close to humans. They're generally only dangerous if they're cornered. Most of the time, if you get too close (say, within 3 or 4 metres) they just hop away.

qwerty

the dropbears are much scarier ;)

PM 2Ring

Maybe double that distance if it's a mother roo with a young joey.

Slereah

What if it is wearing oversized boxing gloves

PM 2Ring

08:13

Call Sylvester

Kangaroos are extremely unaggressive. Yes, they can defend themselves if necessary, but that rarely happens. You really have to work hard to corner an animal that can jump that fast and that high.

Slereah

I'll work hard

I must pet it

PM 2Ring

I used to hand-feed tame roos when I was a kid. I never felt in any danger. They won't randomly bite or scratch.

fqq

@ACuriousMind the wiki pages are pretty good, amaro is a subset of Kräuterlikör. In an English context amaro = italian amaro, amaretto is the almond liquor, amaretti the biscuit

PM 2Ring

Rock wallabies are more fun to interact with than roos. They aren't so skittish, and don't mind being patted. But if you do interact with them and give them food, they won't go away. :) They're extremely agile. They're amazing to watch going up almost vertical cliff faces.

naturallyInconsistent

08:31

@Slereah same

PM 2Ring

They have soft fur. But not quite as soft as alpacas.

naturallyInconsistent

poof poof~

qwerty

i saw some pademelons last year

very cute

PM 2Ring

08:49

Yeah. Rock wallabies are a bit larger, and have a similar temperament to pademelons, but a bit more adventurous.

naturallyInconsistent

you know, rock wallabies give meow meow the impression that they are pokémon...

qwerty

@fqq what do you call a single biscuit? is it still amaretti in the singular?

@PM2Ring Is this true even for the big bucks? I see roos pretty much only when I travel and sometimes the big ones give me the stay away from me look, and I give them a respectful berth

fqq

@qwerty no in italian that would be "un amaretto". whether the singular refer to the liquor or the biscuit depends on context. e.g. "ho voglia di un amaretto" is ambiguous

PM 2Ring

@qwerty Pretty much. They'd rather escape than fight. But definitely don't push your luck if they think you're threatening their joeys...

Tobias Fünke

09:22

morning

qwerty

hallo Tobias :)

Tobias Fünke

@Allie Is your question about the factorization of the partition function resolved? Have you checked the link I've posted?

Ryder Rude

09:36

hi

Tobias Fünke

hello

Signor Feynman

09:52

@SillyGoose I don't know if there are alternate formulations, but those I have seen didn't display anything intrisically unrigorous, I think

Although the partition functions often involve path integrals, but I wouldn't see that as a feature of Wilsonian RG

You don't have such problems on an Ising lattice

qwerty

10:32

I wish chat and phys.SE had inbuilt dark mode. and overleaf too

Tobias Fünke

yeeees

it hurts my eyes lol

Signor Feynman

@qwerty the chat is already dark enough without a dark mode :P

Tobias Fünke

hehe

skullpatrol

11:06

I think there's a dark mode available in the Opera browser.

PM 2Ring

@qwerty Chromium-based browsers have a "Forced Dark" mode. I use it in the Samsung Internet browser on my phone. It mostly works, but not always. And the Samsung Internet version is more quirky than the Chrome version. howtogeek.com/446198/…

qwerty

yeah I use a browser add-on but imo they're not as nice as when the website has designed for it

PM 2Ring

Definitely

Stack Overflow has a dark theme. And a high contrast theme. But SO is somewhat "special", and they can't easily roll out the dark theme to other sites on the network. :(

skullpatrol

:(

qwerty

really? do you know why it's difficult?

PM 2Ring

11:15

Not exactly. They developed a modern User Interface system to make it easier to do stuff on the whole network, and most sites use it. But not Stack Overflow itself. If I understand the situation correctly...

46

Q: Our Design Vision for Stack Overflow and the Stack Exchange network

For those who don’t know me, I’m the Director of Design at Stack Overflow. I’m responsible for the team of designers who work on the public sites. The visuals of Stack Overflow and the network sites have remained largely unchanged since I joined Stack Exchange, Inc. in 2017. The aging design has...

Also see github.com/StackExchange/Stacks

46

A: Dark Mode for Stack Exchange sites

Currently, Dark Mode is available as a beta test on Stack Overflow only. More details can be found in this Meta Stack Overflow question. At the moment, it isn't clear if, how, or when it will be rolled out to other sites in the network: Future releases At this point, the focus of Dark Mode is on...

Ryder Rude

12:14

i have an idea in mind where i distinguish between two types of understanding (which applies to all living creatures). the first kind of understanding is sort of a subconscious understanding. it is when the animal just knows what to do intuitively because of the understanding that evolution has imparted in it

the second kind of understanding is when an animal consciously applies a tool like logic and mathematics to come up with a model to understand the behavior of something

anyone know of some standard ideas which describe this distinction?

what i have in mind is that the first kind of understanding is incomparable across animals, while humans rank above other animals with respect to the second kind of understanding

qwerty

@RyderRude i'm not really keen to discuss it here but you could probably read SEP plato.stanford.edu/entries/epistemology/#SourKnowJust

Ryder Rude

@qwerty nice.. this describes even more categories of understanding

thanks

SnoopyKid

12:43

Do some of you guys here play Escape From Tarkov

Silly Goose

14:27

@SignorFeynman do you have a reference?

I am reading John Cardy's book and it essentially just describes RG as a method in vague detail, with no precise definition of an RG transformation.

just a "if you see it you'll know" sort of thing

Signor Feynman

14:39

@SillyGoose you may take a look at Goldenfeld's lectures, there is a book

Some things are maybe outdated but the description of the RG procedure is quite good

You should be able to find it easily

Silly Goose

17:33

i still don't see a definition of a renormalization group transformation in that text :P

ACuriousMind

@fqq yeah, I read them as amaro being Italian Jägermeister ::shudder:: I was just confused because @SignorFeynman seemed to have a different understanding

Signor Feynman

The only logical explanation is that my understanding was wrong

Slereah

@ACuriousMind Found out the solution to that problem I was having btw

Apparently specifically in the case of stable types, the cofiber and fiber are identical

Signor Feynman

Oh, did you fix that wormhole in your kitchen

Ah, that other problem

Silly Goose

17:49

I am more wondering I guess if RG is actually just a vague notion. Or, if these texts are just vague in their description of RG.

and if RG really is vague, why write any sort of type of textbook on it? if it really is just an example-by-example procedure, then I should just do examples :P

I am wondering if RG can be precisely stated. For example, the principle of stationary action has a precise statement: if a system has an associated action functional $S$ which is a function of the dynamic variables, then the EOM are given by stationizing the action.

Signor Feynman

My knowledge of alcohol is not outstanding to say the least, which is the root of the misinformation I risked spreading. I should be more careful and make less light-hearted and uninformed claims, which take away from my credibility as a part of the scientific community. I apologize for the misunderstanding and I suggest to remove any information I gave on that matter :P @ACuriousMind

Silly Goose

This principle clearly defines what type of mathematical object $S$ is (a functional), how it is connected to the system studied (through its dependence on dynamic variables), and what it gives and how (the EOM by stationizing)

Signor Feynman

@SillyGoose didn't you find the part where RG is described as a 3-step procedure?

Silly Goose

In constrast, RG is presented as (1) suppose there exists some mystical RG transformation $R$ which at the least leaves the partition function of the system Hamiltonian $H$ invariant. Further conditions are not provided. (2) suppose there exists a fixed point, ... etc.

ACuriousMind

@Slereah happy to hear that or sorry that happened to you :P

@SignorFeynman the solution is clearly just to drink more :P

(this is not actual advice)

Slereah

17:55

Not a terribly horrible thing but it probably could have been avoided by writing things explicitely on those articles :p

Silly Goose

@SignorFeynman i don't think i have a problem with understanding the procedure, more with understanding what a "RG transformation" is

I mean there should be a simple definition if it is well-defined.

E.g., A lorentz transformation is an isometry of the minkowski metric

ACuriousMind

@SillyGoose It's the transformation that turns the theory at scale $\Lambda$ to the theory at scale $\Lambda'$, however you implement that, e.g. by integrating out the interval between $\Lambda$ and $\Lambda'$ in the path integral in the Wilsonian formulation

you're probably focusing too hard on the "group" aspect here - algebraically it's very boring, a one-parameter (semi-)group parametrized by the $\Lambda$

Silly Goose

@ACuriousMind okay but there is not a unique object performing this action generally, right?

ACuriousMind

you're not finding anyone discussing this in terms of group structures or whatever you expect because there's just nothing interesting htere

@SillyGoose I don't know what you mean by "unique object"

Silly Goose

i am not interested necessarily in the algebraic structure, but even the definition you presented is vague. what is a theory at scale $\Lambda$ and what does it mean to turn it into a theory at scale $\Lambda'$

Well a first question is: is there really the theory at scale $\Lambda'$

ACuriousMind

17:59

@SillyGoose But that's defined as part of the renormalization procedure itself. Again the exact definition depends on the "flavour" of renormalization you're looking at, e.g. Wilsonian renormalization at hard cutoff $\Lambda$ just is the theory that results from putting some given Lagrangian into the path integral and integrating up to $\Lambda$ in momentum space.

I don't find anything vague about this, as "mysterious" as the actual meaning of this may be

the vagueness you perceive probably arises from people not wanting to tie themselves too closely to some specific implementation of the renormalization procedure (such as Wilsonian with a hard cutoff)

while the solutions to the RG equations (like the $\beta$-functions) depend on the renormalization scheme beyond first order, you can discuss some general properties of renormalization without choosing a specific scheme - I suspect this is what you find vague

so to answer your question: No, there is no "the theory at scale $\Lambda$", as the meaning of "at scale $\Lambda$" depends on the scheme

Silly Goose

@ACuriousMind but if this is all wilsonian renormalization is, then why is there so much written about it. the method itself sounds like just averaging out certain d.o.f.

ACuriousMind

in contexts where it really matters, you will find that the scheme is explicitly specified - e.g. the PDG will tell you what scheme its values for the coupling constants and masses etc. are in

Silly Goose

i mean haven't people been integrating out details that don't matter since the beginning of time

i think this is why i think i misunderstand the method. it doesn't really seem like anything novel as i understand it, but i mean RG is a celebrated thing :P

ACuriousMind

@SillyGoose It's an essential part of extracting actual quantitative predictions from QFT, since as I just said, once you have to state experimental quantities and compare them to theoretical predictions beyond first order, you have to state the scheme, and you have to understand how the couplings run in that scheme.

Silly Goose

so i mean is the important part the actual techniques developed to carry out a RG procedure?

the underlying idea itself seems trivial (to average out d.o.f. that don't matter with respect to some criteria)

ACuriousMind

18:09

There isn't really anything comparable in other parts of physics where the actual value of "physical quantities" depends on such essentially arbitrary schemes, which is why I think it's being written about as such a big deal - it's a strange procedure, compared to everything else

Silly Goose

but...that's how human processing works (it is an arbitrary scheme to process the data of the world)

ACuriousMind

@SillyGoose well, that's the thing - it's not really d.o.f. that "don't matter": The Wilsonian hard cutoff scheme is "simple" as you can actually interpret it that way, but in other schemes the meaning of the scale/cutoff is not that straightforward

Silly Goose

it is all of thought and science

ACuriousMind

but, at least to some extent, we're not losing information by the renormalization procedure, this is not an approximation

Silly Goose

@ACuriousMind okay so there are nontrivially interpretable generalizations of the simple case you described

ACuriousMind

18:11

theoretically the theories at every scale have to result in the same things if you compute them to all orders

it's just that computing to all orders is infeasible, and the running coupling make it possible to compute good approximative values at every scale with just a few orders

Silly Goose

also, are "renormalization" and "renormalization group" separate things?

ACuriousMind

it's just that computing to all orders is infeasible, and the running couplings make it possible to compute good approximative values at every scale with just a few orders

@SillyGoose no, the group is just the collection of "all the renormalization"

Silly Goose

i mean from wilson's original paper, he wanted to make singularities (associated with critical phenomena) more obvious in stat mech. from a QFTist's perspective they want to remove the singularities. so they are kind of wanting to do opposite things.

ACuriousMind

as I said above, one element of the RG is the transformation from the theory at scale $\Lambda$ to the theory at scale $\Lambda'$. The (semi)group aspect is just that it doesn't matter if you go from $\Lambda$ to $\Lambda'$ to $\Lambda''$ or directly from $\Lambda$ to $\Lambda''$

@SillyGoose all I'm saying here is my own hep-th coloured understanding of the issue

Silly Goose

but how can you have a semi-group without "losing information"

if you don't lose information you should be able to define an inverse

ACuriousMind

18:14

it may be different in cond-mat/theories where the cutoff or scale $\Lambda$ has direct physical meaning

Silly Goose

i think there is a direct physical meaning for lattice models in SM at least

ACuriousMind

@SillyGoose The point is more that you can't actually implement that inverse in some of the procedure - like in the hard cutoff case, you can't actually give a prescription for how to "go back" if you don't know where you started from. Intuitively I think of this as the information "lost" being encoded in ever higher orders of perturbation theory as we go to the IR, where eventually it becomes inaccessible due to the asymptotic nature of the perturbation series

(the statement about losing no information above assumes convergence of the perturbation series)

Silly Goose

asymptotic nature as in the perturbation series is an asymptotic series?

ACuriousMind

but take all of this with a grain of salt, renormalization is not a topic I can claim to understand comfortably

@SillyGoose yes

Silly Goose

18:39

what is the meaning of a local operator on a lattice system?

I am trying to understand how general the Hamiltonian (9.37) is, or what motivates considering Hamiltonians of this form.

DIRAC1930

18:50

@SillyGoose If you look in Bogolubov's book, I think he elucidates why it's called a group

Allie

Hi girla

Girls

If we’re just considering one particle with many possible energy states e_1, e_2, etc it is necessarily the case in stat mech that at any temperature, it is most likely to be in state e_1 over any other state right?

Since the relative probability of getting a higher energy state is always lower

Even though the average energy will tend to get higher as the temp increases

I shouldve specified e_1 < e_2 < …

Tobias Fünke

hello

Allie

19:06

Hya tobias

And i guess ill stipulate that the energy levels are nondegenerate

Tobias Fünke

Well, for the canonical ensemble yes. It does not only hold for one particle (which in stat. mech you anyway do not really consider (?)), but for the whole system itself

For a given temperature $T>0$ you have that $P_T(E_1)>P_T(E_2)$ if $E_1<E_2$ and both are non-degenerate... which simply follows from the Boltzmann factor.

Silly Goose

The argument fails at $T\to \infty$ in which the microcanonical ensemble is recovered

Allie

Right

Thanks!!

Signor Feynman

19:43

@ACuriousMind I didn't read this on time and before I knew it I had followed your advice and drank three bottles of Jägermeister

ACuriousMind

20:46

@SignorFeynman rip

Allie

21:30

Meow

Silly Goose

oh my god the notation in these renormalization group books is going to make me kill myself

Signor Feynman

@SillyGoose maybe you should check Weinberg vol 2

This joke will never get old

DIRAC1930

@SillyGoose I don't know why they don't just use a simple toy model, simplified as much as possible

There's a video of Shankar online doing this but the video and audio quality is so low that you can't really make anything out unfortunately

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