The h Bar

Slereah

01:00

Constant acceleration is not fine

Because that would require infinite energy

Phase

proper acceleration?

Well, not infinite if for finite time

0celo7

$D_uu$

Phase

I even conceded in my comment that the energy requirement would be silly

But it was just arguing that "earth accelerating upwards at $g$" is one of the less physically ridiculous arguments FE people make if you ignore the energy required.

Semiclassical

I haven't seen any flat earthers on campus, but

there was a guy with a selfie stick and a sign saying "Satellites do not exist"

0celo7

Daily reminder that anything other than Earth-shape-agnosticism is insane

Slereah

01:04

@Semiclassical Does he not believe in the moon

Phase

Side note

Semiclassical

could not tell you. i didn't linger

0celo7

the next group has order 21

what the hell

Semiclassical

searching "satellites do not exist" on Youtube gives some videos which I fear to look at

0celo7

@ACuriousMind yo what's $\langle a,b| a^7, b^3, bab^{-1}a^{-2}\rangle$?

Semiclassical

01:06

quite a few of them, ugh

0celo7

the name I mean

Phase

Semi

trust me

In flat earth groups the round earth people are just as bad

ACuriousMind

@0celo7 Lol, I cannot discern arbitrary groups from a random presentation of them :P

Phase

No-one knows the difference between speed and velocity, and virtually no-one has ever heard of calculus

Semiclassical

there aren't so many groups of order 21

0celo7

01:08

@Semiclassical I've been staring at various group databases all night

@ACuriousMind how do I semidirect product?

ACuriousMind

@Phase The difference between speed and velocity is a ridiculous one, other languages don't even have two different words for that :P

Phase

He's English

well, american but

fite me @0celo7

Semiclassical

...

Phase

I'll hit you all so hard your words fall back into the correct spelling

God damn it.

0celo7

@Phase America is the greatest nation on Earth by some standards. England/Britain isn't by any.

Phase

01:09

How so?

ACuriousMind

@Phase Racist insults are not okay, even in jest.

Phase

I mean

0celo7

@ACuriousMind Seriously? Americans are not a race!

Phase

I dont really consider american a race

English and Americans are just geographically separated

virtually the same culture

Semiclassical

you're the one who used the word 'subspecies'

Phase

01:10

In jest

0celo7

@ACuriousMind well?

Phase

purely because of the spelling

0celo7

$\rverttimes$

ACuriousMind

@0celo7 By calling them an "inferior subspecies" Phase was implying that. The truth of an insult does not matter for it to be an insult.

0celo7

$\crossprod$

Semiclassical

01:11

I have a hard time thinking of America as 'the greatest nation on earth' these days

0celo7

$\semidirectprod$

Slereah

what crazy symbols are you trying to make

0celo7

@ACuriousMind ???

ACuriousMind

\ltimes and \rtimes

0celo7

$\rtimes$

@ACuriousMind it is $C_7\rtimes C_3$

now how do I compute the character table

Semiclassical

01:13

The fact that 'European' is practically an epithet in American politics is weird to me.

Phase

Europe varies massively too

Well, within sensible limits

Semiclassical

no, see

they're all godless socialists

Phase

Damn I forgot

I mean not for long

NHS is being stabbed in the neck year by year

Semiclassical

huzzah austerity

0celo7

@Semiclassical atheist catholic anarcho-capitalism ftw

Phase

01:15

Soon it'll be like America where if you get shot you also lose your home from the medical bill

@0celo7 To be fair you have to appreciate Rick and Morty to truly Appreciate atheist catholic anarcho-capitalism

0celo7

@Phase don't get shot

Phase

[...copypasta continued]

damn thats good advice

ACuriousMind

@Semiclassical I wish we all were :P

0celo7

rick and morty is ok

Phase

I'll take that to my slightly more delayed grave

R&M is cool, but the fanbase is like a horde of tiny little tumours

Semiclassical

01:16

lol

Slereah

That it is

0celo7

@ACuriousMind if you don't believe in god, what is your moral barometer?

Phase

People literally stabbed each other for szechuan sauce outsides McDonalds

Slereah

But most shows have awful fandoms

Semiclassical

Socialist is, of course, another one of those words which 'mericans use

Slereah

01:16

So no surprise

Semiclassical

Republicans calling Obama socialist was always just hilarious

ACuriousMind

@0celo7 I was not aware morality is measured in Bars

Phase

I think when someone gets stabbed over dipping sauce

The fanbase needs a bit of a check

Slereah

@ACuriousMind Morality is also best at sea level

0celo7

@ACuriousMind it's measured in torr but the terminology for the measuring device is historical

Slereah

01:18

I measure my morality in millimeters of mercury

0celo7

@Semiclassical anyone who takes my money at gunpoint is socialist

Trump is socialist, though less socialist than Obama.

Phase

If you don't believe in god who will tell you who won Miss Universe

0celo7

Or maybe more, I can't really tell what he's up to

Trump has mastered the tactic of mass confusion

ACuriousMind

@Slereah And here I thought wise and enlightened people always lived on mountains

Slereah

they are wise, just immoral

0celo7

01:19

@ACuriousMind what the hell does this mean

Phase

@0celo7 please don't use the term hell I'm religious and it offends me

0celo7

@Phase too bad!

Phase

bAMPERSAND

0celo7

I'm deeply religious but don't believe in god. It's an interesting state of mind.

Phase

Do you believe in the vibrational quantum consciousness god?

0celo7

01:21

No

Phase

heretic

0celo7

I believe in the green god aka the dollar

Semiclassical

water has memory, dontcha know

0celo7

Actually no, the dollar is fiat currency

Phase

sit down @0celo7

be humble

0celo7

01:21

I believe in the yellow god, ~~piss~~ gold

@ACuriousMind halp

Phase

I hope you're asking him for help with maths and not worshiping your god

0celo7

yes

@ACuriousMind I can't into algebra and I made a huge mistake taking this class

Phase

I know that was intentional but saying yes to a multiple choice still amgery's me.

0celo7

oh it wasn't

ACuriousMind

@0celo7 I don't see what I'm supposed to do about that :P

0celo7

01:24

I mentally pointed at one and said yes

@ACuriousMind are you upset about the barometer meme?

it was a meme, rest easy

Shit Steve Harvey Says

►

@ACuriousMind I don't know what that sentence above means..

ACuriousMind

@0celo7 I'm not sure either. It sounds as if it's saying $ba = a^2$, which would mean $b=a$ and makes no sense.

Phase

the brain in the jar has reached a verdict

download that pdf onto a USB stick, remove it and suplex it

Semiclassical

what was the group presentation?

0celo7

$\langle a,b|a^7=b^3=1, bab^{-1}=a^2\rangle$

Semiclassical

hmm

0celo7

01:28

@ACuriousMind is he just saying that conjugation aut by $b$ squares $a$?

ACuriousMind

Ah, they mean $b$ acting by conjugation

0celo7

@ACuriousMind Ugh I think I need Sylow for what follows

I don't know Sylow

Phase

I think I'm just gonna have to

eat doodoo and move on from that FE thread. You cant convince some people

Anyone else enjoy torturing themselves with that like I do?

Semiclassical

The law of holes: "If you're in a hole, stop digging."

0celo7

just dig through to Chyna

Donald Trump Says "China"

►

Phase

01:32

Oh good thanks Ocelot i totally didnt get the reference

2

$\mathcal{[S A R C A S M]}$

Semiclassical

on another matter entirely

i saw this problem lately

Phase

Mathcal is such a nice font.

0celo7

@ACuriousMind and that function has "order" 3? So what?

Is that a hint to use some Sylow stuff

Semiclassical

You must build a very specific tower out of four differently colored pieces that can be stacked in any order. But when you start building, you don’t know what the correct order is.

Upon assembling the pieces in some order, you can consult an architectural oracle (he goes by Frank) who will inform you if zero, one, two or all four pieces of the tower are in the correct position. Your tower doesn’t count as finished until the oracle confirms your solution is correct. How many times should you have to consult the oracle, in the worst case, to assemble the tower correctly?

ACuriousMind

@0celo7 I don't know, I have no context to decide why the author is saying that!

Phase

01:35

In the worst case you're blind, deaf and cant feel touch, so you'd not consult him at all

simple

0celo7

@ACuriousMind character tables

Semiclassical

No, in the worst-case you're a smart a** and you make up stuff rather than actually try the question :P

Phase

In the worst case I flag your statement and summon the beast known as the mysterious shog to destroy your soul

0celo7

the algebra nerds in class were whispering about Sylow and short exact sequences and I have no idea what they're talking about

Phase

Idk why my brain keeps autocorrecting statement to question

Semiclassical

01:36

back later

Phase

Cya dude

Could someone help me understand calc of variations? There's a bit of confusion I have regarding why functions aren't considered to have a range $\mathcal R$

0celo7

I'm an expert

what is the doubt

Phase

www2.math.uu.se/~gunnar/varcalc.pdf

The footnote on page 4

I don't see why it's true

is it saying that not ALL functions map to real numbers?

Because if so, couldn't you just as easily define a non real functional that means that not ALL functionals have to map to R either?

0celo7

I have no clue what they're trying to say

Phase

oh

RIP

could you pls recommend a better, but not masochistic source for me to read?

0celo7

01:44

I think I know what they want to say but it's not at all what they wrote

@Phase ...

idk

Phase

if not then no worries

0celo7

nothing not masochistic

Goldstein probably explains it

Phase

just something that is rigorous without skipping important steps is what I mean by that

Side note

What does it mean for a function to be defined as "identically zero" on a subset of a domain

just that it's zero everywhere?

0celo7

ask ACM, I'm trying not to fail a class rn

sorry

Phase

No worries, good luck fam

@ACuriousMind I summon thee, I beseech thee help me with my basic question

[sacrifices lamb]

[sacrifices another lamb]

ACuriousMind

01:51

@Phase Yes

0celo7

oh jesus christ

$4$ is a cube root of unity in $\Bbb F_7$

what a mess

bolbteppa

02:06

@Phase the footnote makes no sense, use Gelfand

0celo7

02:54

@BernardoMeurer she is from your area youtube.com/watch?v=PEGccV-NOm8

Bernardo Meurer

@0celo7 Not interested

0celo7

wow

@ACuriousMind are you still here?

I need a 3x3 complex rep of $C_3$

probably just a rotation by $120$ degrees in a plane

Slereah

@ACuriousMind still around?

Mama mia

0celo7

@Semiclassical YYYYYYEEEEEEESSSSS I GUESSED THE LAST REPRESENTATION

I think this is a spin 1 matrix actually. QM ftw

@Slereah do you think I cannot answer?

Slereah

@0celo7 Riddle me this Batman

What's the connection form of the product of two groups

That is, take the weak and strong interaction

0celo7

03:06

additive

Slereah

$SU(2)$ and $SU(3)$

Usually these are denoted as $d + G + W$

0celo7

it adds

yes

Slereah

With the gluon field and the weak field

But then, the particles are like

$\psi_{w}$ and $\psi_s$

You get a doublet for $SU(2)$ and a triplet for $SU(3)$

But how can both of those be applied if it's additive

I would think that the spinor would be something like $\psi_{ws}$

Where you can rotate the weak charge and the color independantly

But then what sense does the weak index make when applied to the gluon field

0celo7

ugh since when are you so interested in phenomenology?

ACuriousMind

@Slereah Given a representation $V,\rho$ of $G$ and $W,\sigma$ of $H$, the natural representation of $G\times H$ associated to this is $V\otimes W$. The representation of the Lie algebra $\mathfrak{g}\oplus\mathfrak{h}$ on $V\otimes W$ is given by $(g,h)\mapsto g\otimes \mathbf{1}_W + \mathbf{1}_V\otimes h$.

Slereah

03:11

No phenomenology here

It's all math

ACuriousMind

The physicist (and the sloppy mathematician) usually drops the tensoring with the identities, so you see $g+h$ although it strictly speaking makes no sense.

Slereah

So how would you write the derivative in that case?

Is it $G \otimes 1_w$?

and $1_s \otimes W$

0celo7

@ACuriousMind Oh no, I have committed the sloppy mathematician sin

Slereah

You must be cast down to hell

0celo7

@Slereah Something like that. It's like writing $g+h$ for a metric on $M\times N$

Slereah

03:14

Makes sense I s'ppose

0celo7

Many people write $g\oplus h$ to make it clear that there's no addition going on

You need to split up the vectors, then feed them in, then add

Slereah

So I guess that with indexes it would be like $\tau_\alpha \sigma_\beta G_\mu^\alpha I^\beta$

Plus the matrix indexes for $\tau$ and $\sigma$

ACuriousMind

@Slereah What's $I$?

Slereah

Identity matrix?

ACuriousMind

Then that expression doesn't make any sense :P

Slereah

03:17

Oh wait, I guess it would just be like...

$\tau^{ab}_\alpha G^\alpha_\mu I^{cd}$

or something

ACuriousMind

You're being unnecessarily complicated. You have a tensor $\psi_w^a \psi_s^b$, and you simply apply $d + G + W$ by letting $G$ act on the $\psi_s$ and $W$ on the $\psi_w$.

Slereah

What if I want to be unnecessarily complicated!

0celo7

@ACuriousMind isn't that what I said

Slereah

(I'm working on that old idea I had to put every index ever on an equation)

ACuriousMind

@0celo7 In spirit perhaps, but you discussed a case where the vector we're applying the "$g\oplus h$" is not a tensor product but a direct sum.

0celo7

03:22

$\oplus$ is just a functorial operation on $\mathsf{Vect}$, as is $\otimes$

so in spirit it was definitely there

ACuriousMind

@Slereah Take a very long look at how Weinberg's equations look. Then rethink your idea :P

Slereah

Which ones

0celo7

ok Weinberg's notation isn't bad

Slereah

He's got a lot of them

Semiclassical

@0celo7 nice

0celo7

03:24

@Semiclassical it's not, I misremembered it :P

Slereah

My book 2 of Weinberg's QFT got some water damage so it is not pleasant to paw through

Semiclassical

aww

0celo7

but it worked out so ::shrug::

Semiclassical

what did it turn out to be?

0celo7

Semiclassical

03:25

huh

i can see why you thought of s=1, at least

Sir Cumference

How do I log out of SE on other computers?

0celo7

@SirCumference delete your account

Sir Cumference

@0celo7 ...

Semiclassical

...

Sir Cumference

My cousin keeps posting dumb things under my name

0celo7

03:26

@SirCumference reset the password.

Sir Cumference

will that kick him out?

0celo7

it will force a log in for all users

ACuriousMind

@SirCumference When you log out (on the desktop site), you can check a box "log out on all devices" on the log out screen.

0celo7

or that

Sir Cumference

ah, thanks

0celo7

03:27

but best to change the pw anyway

if it's his computer he will probably know the pw

Sir Cumference

I think I was logged in when I came back home and never logged out

Slereah

What happened to you, Weinberg

Semiclassical

"YOU HAPPENED TO ME"

Sir Cumference

Now he's posting things like "Poll: Is Nyan Cat a dog or a cat??" on pets

0celo7

my Bott and Tu has some water damage

nothing like that though

jeez

Sir Cumference

03:29

and "Ground Control to Major Tom...Your circuits dead, there's something wrong.... Can you hear me Major Tom?" on Astro

ACuriousMind

@SirCumference You don't have an account on Pets.

Sir Cumference

@ACuriousMind I removed it after I noticed something sketchy

0celo7

rekt

ACM caught you in a lie

Sir Cumference

I thought my account was hijacked, but no, he confirmed it

@0celo7 ok

Semiclassical

weirdly enough, I've had "Space Oddity" stuck in my head tonight

0celo7

03:30

@ACuriousMind can you confirm?

Semiclassical

synchronicity

Slereah

@ACuriousMind what do you mean about Weinberg

Things don't seem peculiar vis à vis the notation

0celo7

ACM is scared of indices

ACuriousMind

@Slereah The QFT book has an ungodly proliferation of indices

Semiclassical

@0celo7 I need an expert opinion: Is the latest message in the Math chat basically just baiting?

Slereah

03:32

Those seem pretty normal

Much less bad than say Siegl's book

Semiclassical

I feel like it's trying to troll but it's so non-specific as to be headscratching

Slereah

where he does spinor indexes too

0celo7

@Semiclassical what the hell is that supposed to mean?

Sir Cumference

@Semiclassical what message

Slereah

I think math people don't like indices because they don't actually have to calculate quantities

0celo7

03:33

@Slereah speak for yourself

Semiclassical

:/

0celo7

as the only actual mathematician in here I can say we love indices

Sir Cumference

@0celo7 You're a college student...

0celo7

@SirCumference that's what you think

Sir Cumference

what

Is ocelo really a 35 year old mathematician?

Slereah

03:35

Well that would explain some things

3

Q: Formal definition of gauge field and spinors in QFT

I am trying to pin down what spaces a spinor and gluon gauge field exactly occupy. I know that the spinor is a quantity $\psi_{i\alpha f}(\vec x, t)$ where $i$ is a color index in the fundamental representation of the color group $\mathrm{SU}(N_\mathrm c)$, taking 3 different values; $\alpha$ i...

Pretty close question to what I'm wondering

Semiclassical

$$\psi \colon \mathbb R^{1,3} \mapsto \mathfrak{su}(N_\mathrm c) \otimes \Lambda^1\,\mathrm{SU}(N_\mathrm f) \otimes\Lambda \mathbb C \otimes \Lambda^1 \mathbb R^{1,3} \,.$$

oof

Sir Cumference

is that not simple enough for you?

0celo7

@Semiclassical are you implying I'm an expert troll? Because that's Not Nice

Semiclassical

:)

Slereah

$\mathrm{SU}(CC)$

0celo7

03:38

@Semiclassical the $\Lambda\Bbb C$ is basically just there for trolling purposes

Sir Cumference

Holy crap I forgot to pick up my laundry from yesterday...

0celo7

what the hell are there $\Lambda$s for anyway

@SirCumference looooooooooooooooooooooooooooooooooooooooooooooool

go get it!

Semiclassical

one-forms something something?

Slereah

I'm guessing the last one stands for a one-form

Sir Cumference

I am...

Slereah

03:39

Not a clue what $\Lambda \mathbb C$ is for though

0celo7

$\Lambda\Bbb C\cong\Bbb C$

Slereah

From his question it seems to be the Grassmann field, maybe?

0celo7

huh

Slereah

But that's not how you denote it

0celo7

well, screw physics

3

Slereah

03:40

I don't think

Semiclassical

we're trusting they wrote it right, of course

Slereah

Also why is the color $SU(3)$ but the flavor is $\Lambda^1 SU(6)$

Why the random lambda

0celo7

ask @ACuriousMind

dmckee

@0celo7 ::chuckles:: That's the kind of mistake you don't forget in a hurry.

Slereah

I'm guessing the answer isn't in @ACuriousMind's mind but the twisted mind of that poster

ACuriousMind

03:42

@Slereah The asker is a bit confused and the expression he wrote down there doesn't really make sense

Slereah

yeah it's kind of a mess

0celo7

@ACuriousMind yo bub what's the symbol for conjugacy class

Slereah

What would be the set a standard model spinor belongs to?

Is it just $ \mathbb{C}^{4 \times 3 \times 2 \times 1}$

Sir Cumference

@0celo7 Checked...my laundry is gone...

0celo7

@SirCumference are you trolling?

Sir Cumference

03:53

I swear I'm not

Never mind, I'm a moron

It's still here, I checked the wrong machine...

0celo7

how are you still alive?

Sir Cumference

At this point I think I'm losing it...

John Rennie

@0celo7 You have my sympathy. We've all made that mistake, but we usually only make it once :-)

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