The h Bar

Allie

00:15

hi girls

bolbteppa

01:05

If you know what you're doing, and don't mind it making a ton of mistakes, you can really use gpt to revise some basic stuff you should know

Allie

01:41

yeah im never gonna do that

id rather consult resources made by humans who know exactly what theyre doing then sift through a computers mistakes

Tobias Fünke

06:12

@SignorFeynman hehe

classic SF move ;)

naturallyInconsistent

06:31

sci fi? signore? Isn't he soon to change his username?

qwerty

I now have zotero beta with WebDAV syncing all my files on my phone \o/ all of my library is now in my pocket

naturallyInconsistent

06:55

where if you use it, you will go blind from all the tiny fonts~

miehehehe

qwerty

X_x

I'm reading a textbook at a bus stop because 2 buses in a row got cancelled lol

naturallyInconsistent

08:04

Why and how do buses get cancelled? hmm

Slereah

"There is a deep sense in which stable homotopy theory is analogous to linear algebra, namely Goodwillie’s calculus of functors, and it has been argued that from this point of view at least $\Omega^\infty \circ \Sigma^\infty$ is indeed the analogue of the exponential function."

Whaaat

Madder

10:11

Hello i have exactly the same request as this person
https://math.stackexchange.com/questions/3451152/reference-for-onsager-s-solution-of-the-2d-ising-model

and i am not finding any resources that explain the original solution as it was presented

Ryder Rude

10:39

hi

skullpatrol

11:28

hi

qwerty

12:08

en.wikipedia.org/wiki/Domain_coloring these are the prettiest plots i've ever seen

Feynmate

12:37

@naturallyInconsistent I have already done the deed

qwerty

FEYNMATE

3

imbAF

13:38

How to understand noether current? The only knowledge I have is that of a current or current density of electric charges passing through a cross section per unit of time

Can the same interpretation be done for noether charge and current?

Slereah

14:06

"Moreover, according to deformation theory a pointed space is affine if it is infinitesimally extended, which by the above means it is orthogonal to ∮-modal types."

Gonna die reading that paper

Feynmate

14:40

You may wanna buy a Noether multimeter

The formalism for currents is always the same, be it electric or not. You have some physical quantity flowing and a corresponding density and current that satisfy a continuity equation, which has always the same form

One example is the current of probability you know from QM:
$\rho=\lvert\Psi\rvert^2, \vec{j}=\frac{\hbar}{2mi}[\Psi^\ast\nabla\Psi-\Psi\nabla\Psi^\ast]$ and $\partial_t\rho+\nabla\cdot\vec{j}=0$

naturallyInconsistent

15:03

@Feynmate doo doo doo dooo

Feynmate

15:39

@qwerty Oi mate

Tobias Fünke

lol

Allie

hiiiii

PM 2Ring

16:00

@qwerty That looks nicer than the old style plots, which use a fully saturated HSV palette. The new style uses less saturated colours from a more perceptually uniform colour space, probably CIELAB, or maybe CIELUV. LAB is suited to printed pigments, LUV is suited to screen pixels. A newer option is Oklab en.wikipedia.org/wiki/Oklab_color_space

I just made that cycle using a Oklab / Oklch script I wrote last year. The luminance is 0.75, the chroma is 0.1

Jul 1, 2024 at 6:49, by PM 2Ring

I also made a thing for plotting complex functions (of a single variable) in 3D. The norm maps to the height, the arg maps to a colour in a spectral cycle. So the (default) identity function maps to a rainbow cone. You can give arbitrary expressions & functions in the input box. Sage has a lot of built-in functions, and most of them should work. (Some don't work with symbolic variables, only numeric values). https://doc.sagemath.org/html/en/reference/functions/index.html

The Sage script is linked in my post following that one. It just uses a HSV palette, but it's not hard to edit it to use a different palette

Allie

tobias hiyas

Tobias Fünke

Hello

I am currently at work and just passing by hehe

Allie

not sure if i answered ur question the other day, yes I am still working in DFT

PM 2Ring

I lied. It uses a CIELUV palette. :) But it's still pretty intense.

ACuriousMind

@qwerty synchronicity - my bus this morning was also cancelled/very delayed!

Tobias Fünke

16:14

@Allie I asked if the partition function problem/question was settled, about the factorization.

^^ but no worries

Feynmate

16:46

@ACuriousMind maybe it was the same line (?)

ACuriousMind

@Feynmate I don't think there's a bus line connecting Germany and Australia :P

2

Feynmate

Oh great, now ACM also has a bus-line expertise

meowdib

17:04

Is anyone into de Sitter string theory?

nvm bye

ACuriousMind

@Feynmate given that I don't have a car and use a lot of public transport: Yes, actually, I have :P

User198

@Feynmate xD

Ryder Rude

18:19

hi

the caonical momentum is a section of $T^*(TM)$. do we use the projection map $\pi : TM \to M$ to make canonical momentum a section of $T^*M$?

Ryder Rude

18:46

but the pullback by $\pi$ can only map elements of $T*M$ to elements of $T*(TM)$

LittleBlue

Does anybody here knows a good book or article to learn dimensional reduction in QFT?

Ryder Rude

we want to map a section of $T^*(TM)$ into $T*M$ somehow

i think we want to map a section of $T*(TM)$ which is $\frac{\partial L}{\partial v}$ into points on $T^*M$

ACuriousMind

@LittleBlue Do you really mean QFT or do you mean in the context of string theory?

LittleBlue

@ACuriousMind in QFT.

I am using a package for wolfram Mathematica that performs that in my Lagrangian and I wanted to understand better what is happening.

ACuriousMind

then you probably should look for "Kaluza-Klein" as a buzzword, but it's not really a large topic on its own - without the additional complications through string theory you really just decompose the higher-dimensional fields into appropriate lower-dimensional ones

(there's lots of stuff where people study specific reductions of specific theories, but I don't know a lot of things dealing with the "generic" theory )

really 95% of the time I've seen dimensional reduction it's in a stringy context because they're doing compactification

LittleBlue

18:57

Ohh okok.

I am using it to make the computation of beta functions, etc more easier.

ACuriousMind

so another way might be to take an intro-to-string-theory text, read the chapter on compactification and ignore the stringy stuff (mostly related to branes), but I don't know how well that works if you don't already know string theory :P

LittleBlue

Yea ahahahha

The article of the package talks about dimensional reduction but I am not expert on QFT to understand well a resume.

Ryder Rude

an element of $ T_x^*(TQ)$ is a function from $T_x (TQ)$ to $R$

ACuriousMind

@RyderRude The canonical momentum is not a section of $T^\ast TM$, it's a coordinate of $T^\ast M$. If you mean to ask how to formalize the Legendre transform that in coordinates is $\frac{\partial L}{\partial \dot{q}} = p$, see Legendre transform on arbitrary vector bundles.

Ryder Rude

@ACuriousMind yes. i want to know how the equality is realised. thanks

Ryder Rude

19:15

this means that the formula $\frac{\partial L}{\partial v}$ need not be interpreted to give a section of $T^*(TM)$

this formula just defines the co ordinate version of the Legendre transform map

imbAF

19:55

Can the noether current and charge be understood like the electric charge and current ?

If transformations that change the value of the function represent internal symmetries, is there a name for transformations that change the argument, i.e spacetime argument. I've read somewhere that these transformations are called linear symmetries, but I am not sure

Feynmate

5 hours ago, by Feynmate

The formalism for currents is always the same, be it electric or not. You have some physical quantity flowing and a corresponding density and current that satisfy a continuity equation, which has always the same form

imbAF

but what to understand with flow of angular momentum as the noether charge?

How to understand something like this

And for example when the conserved quantity is energy, the charge is the energy and the 3D current is the energy momentum tensor, if I am not mistaken

Feynmate

So, angular momentum density is a function of spacetime. Take a given region, it will enclose some given angular momentum at a given time. But in general, over time such angular momentum changes and "flows" outside/inside

imbAF

that's a very electric charge/current way of interpreting it. But I guess it is simple, or at least tries to give meaning to such an abstract concept

Feynmate

20:11

Try to see it the other way around. Replace every "angular momentum" in my sentence with "electric charge". If it now it makes sense, then if will also make sense for angular momentum, for mathematically it's the same thing

imbAF

Yes it does

but visualizing both cases is quite different. You can imagine a charge enclosed in some space, whose amount changes over time. Doing the same for the angular momentum is a bit difficult

I'd say it is equally easy the visualize it for the energy, as the energy density changing over time

Feynmate

@imbAF Can your eyes see electric charge density?

Okay, you're probably imagining a charged particle, which carries electric charge and you see this particle going in/out of the box, right?

imbAF

No, but you can imagine a blob of mass, with charge, whose amount (volume it takes in space) changes over time. But I guess this is a naive way to visualize the whole thing

@Feynmate yeah\

Feynmate

@imbAF Then, if you want to go by this simple visualization, just remember that your particle carries angular momentum as well because of its motion

So if it goes out of the box, angular momentum is flowing out

imbAF

Ah, and as particles fly out or in, the total angular momentum changes

Tobias Fünke

20:17

I have never thought about such literal meanings in physics, I think. I don't know if this is a good or bad thing to (not) do

Feynmate

In this particular case, I think it's not that abstract. Or rather, as long as you understand it for mass and charge, you also understand it for angular momentum, energy and momentum

imbAF

It is certainly annoying to have to do that all the time. Or try to trick yourself into visualizing something, so it "makes sense" to you

But it helps me

Feynmate

If you take some time and think about it, you will understand that there is nothing more obvious about the case of electric charge, it's really the same thing

imbAF

Yes I fully understand now

It can be quantity x and flow of x and x can be whatever quantity that is conserved

Feynmate

You have a physical quantity that is not uniform in space but total value (over all space) is conserved, so if it decreases in one region, it means it has flowed into another region, that's the physical meaning of a continuity equation

ACuriousMind

20:20

@TobiasFünke no, it's not (e.g. the EM field also carries angular momentum, so the flow of angular momentum is not literally particles in every case :P)

Feynmate

Of course I tried to stress that it's really pictorial

The proper understanding comes in terms of densities. The particle is just a way to help imbAF understand what it means that angular momentum flows

Tobias Fünke

@ACuriousMind it is not what? A good or a bad thing :p?

ah I see

Feynmate

yeah np mate

ACuriousMind

@TobiasFünke I mean I don't think it's a good habit to insist on every "abstract" thing having a direct and "visual" (or "intuitive") meaning. It works to some extent but at some point you have to either give it up or you get people thinking Feynman diagrams represent particles moving through space :P (This doesn't mean such interpretations can't be useful in specific cases)

Feynmate

Virtual particles moving through space

:D

Tobias Fünke

20:26

yes I fully agree, ACM

Is it just me or in the last week we got much much more very bad questions (which were also more or less heavily downvoted)?

Feynmate

Wow, cucumber really quit

I think we haven't seen a message ever since

imbAF

@ACuriousMind When something is abstract and you don't understand it but mathematically you do, you simply do not care how that translates in nature?

Tobias Fünke

I've chatted with them about a question of theirs some weeks ago

but yes, they did not come back here :(

Feynmate

@imbAF The fact is these analogies are dangerous because they may mislead you. I think they are ok, so long as you don't take the example too literally

Tobias Fünke

@imbAF "translates in nature"???

Feynmate

20:32

@TobiasFünke I assume you mean in a chat on the site

Tobias Fünke

in a specific chat room

yes

sorry. "chatting" in german usually means: writing in a chat (online)

Feynmate

@TobiasFünke Don't worry, I think everywhere in the world except in English speaking countries

Tobias Fünke

haha ok

Allie

hi guys

motivation is hard

i dont want to do this stupid lab report

im so excited to be done with undergrad this semester!!!!

imbAF

I think people out of germany also say chatting

Feynmate

20:34

The focus of my reply was on the site (this site)

As opposed to another site

@Allie don't

Allie

nooo

Feynmate

follow me for more advice

Allie

i cant fail my classes

i just want to study solid state rn :(

not work on a stupid lab report

ACuriousMind

@imbAF That is not what I said.

imbAF

Then what is your way of trying to make sense of something quite abstract but that you encounter in nature ?

Feynmate

20:37

ACM, do you subscribe to the current of thought according to which adding a full stop "." at the end of a message makes it more stern?

Tobias Fünke

haha

ACuriousMind

@Feynmate yes :P

Feynmate

I wonder why this is such an international thing. There is no such thing for other punctuation symbols

Tobias Fünke

@Allie yeah ikr this feeling. However, at some point you will miss being a student :p

ACuriousMind

(unless the message is more than one sentence, then it carries no (or much less) additional weight)

Tobias Fünke

20:38

Indeed.

Feynmate

Yes, of course I only mean a full stop at the very end.

ACuriousMind

@imbAF I'm afraid I have no idea what this question means

I'm not walking around encountering Noether currents or Feynman diagrams "in nature" :P

imbAF

lol it's not what I meant

Feynmate

You're encountering them on Nature

ACuriousMind

heyooo

Feynmate

20:42

New reaction unlocked

ACuriousMind

I'm just Slereah-posting

Feynmate

According to the search bar, that's a very Slereah thing

Damn it

ACuriousMind

lol

Allie

@TobiasFünke everyone keeps saying thi

but i disagre

besides ill still be a student for the next 5 years, no? a phd student

Tobias Fünke

21:03

at least in Germany being a PhD student is quite different from being a student (bachelor +master)

imbAF

In that you go taxation class 5 but get minimum payment xD

fqq

@Feynmate yes.

imbAF

22:54

In the lecture I had about the Lagrange density, it was said that one of the conditions or criteria of $\mathcal{L}$ is that: It must be local (i.e polynomial in fields and derivatives).

While I understand the necessity for it to be polynomial, which means it contains even power of fields and their derivatives i.e real scalar field as an example. And that it somehow is related to renormalizability (which we did not learn about this semester), I don't understand the necessity for it to be local, or rather what it means to be local? That the field is a function of spacetime?

Or perhaps locality implies what is written in the brackets. But if that is the case, I can't see how locality is related to the polynomial nature of it

I am unsure what local means. This is the root of my confusion

Feynmate

23:57

@imbAF here

imbAF

thanks

@Feynmate Do you have any links, for a detailed explanation of Noethers current in CM, in lagrangian, Hamiltonian, examples of conservations, specially energy-momentum tensor? While I have a good understanding

I'd like to refresh my memory on some key stuff

Transcript for