The h Bar

Is there a name for the PDE that looks like the heat equation, except the Laplacian is replaced with the standard spin-1/2 Dirac operator in the plane? That is: is there a name for this equation du(x,t)/dt=Du(x,t) where $D=-i(\sigma_x\partial_x + \sigma_y\partial_y)$ is the Dirac operator.

Similarly, does any have any references where I could learn about the fundamental solutions to this differential equation?

DanielSank

6:35 PM

Ha! Cited myself in an answer

2

Bernard Meurer

@DanielSank Smartass

NeuroFuzzy

6:55 PM

@ArmendVeseli It can't always be solved exactly! If $x''(t)=-\frac{1}{x(t)^2}$, you're not going to have a simple answer , and you'll have to resort to special functions or numerics

Sir Cumference

7:13 PM

@DanielSank Isn't citing yourself in your own answer just redundant?

You're not getting confirmation from another source

peterh

@Shing Your this sentence is unclear to me, give more details.

DanielSank

@SirCumference well, citing a paper gives the reader a lot more information than I'm willing to type into the answer box.

Sir Cumference

@DanielSank True

MonaLisaOverdrive

7:53 PM

'lo again. Just dropping in to see if I've got the right books from the authors recommended last week

amzn.to/2bQZ4My and amzn.to/2bJK9QF

dmckee

@DanielSank Always a lot of fun.

dmckee

8:35 PM

Hmmm ... I suspect it is too early to expect anything, but I am curious to hear what, if any, progress you've made with the reviewer/editor.

NeuroFuzzy

@MonaLisaOverdrive Looks good for a course on nonrelativistic QM! Note that Sakurai died in the process of that book, so some of the later chapters aren't written by him, only based off of /incorporating his notes. I can't comment on shankar since I've never read it.

0celo7

Shankar is amazing

One of two physics books worth reading imo

0celo7

9:03 PM

@dmckee Have you heard of "Packback"

MonaLisaOverdrive

9:15 PM

Good to know @NeuroFuzzy and @Ocelo7. Thanks!

dmckee

No.

Google seems to suggest some kind of textbook rental platform.

0celo7

specifically "packback questions"

dmckee

::shrug:: They want you to sign up to even look around. That always puts me off.

0celo7

@dmckee I wonder who in our physics department decided this was a good idea.

It's basically a forced PSE for the class

you have to ask and answer questions for a grade

Sir Cumference

Howdy...again

@dmckee Say, you're good with astronomy right?

dmckee

9:29 PM

@SirCumference I'm not an astronomer, but I have enough interest to know this and that.

0celo7

@SirCumference you've asked literally everyone that

find a prof or grad student at your school to annoy

Sir Cumference

All right, well is the velocity dispersion of a star cluster simply the standard deviation of the stars' velocities?

@0celo7 Easier said than done

Crap

0celo7

Easier done?

Well shit, do it then.

Sir Cumference

I'm tired

DanielSank

@dmckee re-submitted yesterday.

dmckee

9:31 PM

@SirCumference That'd be my guess, but I don't know if it is the practice.

Sir Cumference

@dmckee All right. @HDE226868 Might you know?

I suppose Chris White is still celebrating his PhD

Congrats to him

DanielSank

@SirCumference the rumor is that he's been on a bender ever since...

Sir Cumference

@DanielSank So I've heard

0celo7

@SirCumference what do Canadians know about astronomy?

DanielSank

What a weird question

Sir Cumference

9:35 PM

Well they can see aurorae better...

Dunno if that counts as astronomy tho

dmckee

@DanielSank My bender was short lived but intense. I was green the next day.

Never again.

Sir Cumference

@dmckee What was it for?

Legends say that when we need Chris White most, he will return

dmckee

I mean the one following my defense. That's the biggest one most academics have for something happy.

NeuroFuzzy

@0celo7 Hah! That sucks.

0celo7

@NeuroFuzzy I asked a question about the superposition principle, i.e. why don't the various charges interact

we'll see if I get a coherent answer

Sir Cumference

9:41 PM

Well, it's basically like here

Except instead of rep, you get a grade

0celo7

yeah, 10 freaking percent of the final grade is this website

NeuroFuzzy

and instead of curating content for the current and all future askers, you're curating content for your professor (or TA, more likely)

as usual!

Sir Cumference

@0celo7 Just ask one of the popular questions from this site

Like this

-17

Q: How can magic be explained with Physics?

Assuming that, hypothetically, and for this example only, "magic" means things like magical powers. In movies, games, etc. we witness magic; however, it's never explained how it works with regards to the likeness world in which they take place in to ours. My wonderng is, how can magic be explai...

@SirCumference well

Or this

9:43 PM

I answered a question on "electrons with the opposite charge"

Sir Cumference

-18

Q: If there is no gravity on the moon why is the american flag waving?

If there is no gravity on the moon, how could this flag be flapping in the wind? (see link) http://www.stumbleupon.com/su/2wD6eg/hea-www.harvard.edu/~fine/images/desktops/Armstrong.jpg

space moon

DanielSank

@dmckee ooof. Sounds rough.

0celo7

someone asked what would happen if we turned off gravity

Sir Cumference

That's an odd question

dmckee

@0celo7 My advisor is a much larger man than I am.

So is his favorite drinking buddy.

They were buying.

0celo7

9:44 PM

what

wrong person?

dmckee

Yeah.

DanielSank

Yes

Jinx

Sir Cumference

@0celo7 All right, I think I've got the best question

Ask this, you'll get an A for sure

0celo7

interesting factoid: If $X\subset \Bbb R^{n+1}-\{0\}$ is compact and intersects each half-line through the origin exactly once, it is homeomorphic to the sphere $S^n$

dmckee

Only drow elves could wield it.

NeuroFuzzy

9:46 PM

(pure evil)

dmckee

And axion faires. But they are rare in this age of the world.

Sir Cumference

I love how it had 2 upvotes

DanielSank

@dmckee "They were buying", and you were still in "consume free calories" grad student mode ;)

Sir Cumference

I've actually seen a lot of funny-bad questions

dmckee

Oh, I wonder who the answerer could possibly be?

Sir Cumference

9:49 PM

Then there are the awful answers

0celo7

@dmckee huh?

Sir Cumference

@dmckee Yep, it was obviously the OP

dmckee

It occurs to me that an official Stack Exchange Wall of Shame would never happen, but an unofficial one might be popular.

0celo7

I haven't been suspended in a few months

what's up with that

dmckee

The mods have gone soft, you've become sneakier, or you aren't hanging around with evil company anymore?

NeuroFuzzy

9:55 PM

Bah! Mods these days.

0celo7

I think it's because David Z isn't around as much these days

Sir Cumference

Ya know, I had a weird dream last night.

About this chat

0celo7

just stop

Sir Cumference

Where it was an actual bar and 0celo was the bartender, but he refused to serve me a drink unless I could answer his riddle

0celo7

unless I was the God Emperor

oh that works too

Sir Cumference

9:58 PM

Which involved some formula with hieroglyphics

And the answer had two decimal points

peterh

@dmckee and a "wall of fun" could get maybe even a quasi-official approval.

0celo7

@SirCumference I'm a $5$-dimensional connected abelian Lie group with fundamental group $\Bbb Z^3$, what am I?

Sir Cumference

@0celo7 driving me nuts

0celo7

wrong.

try again

Sir Cumference

But really, I was trying to escape from the stackexchange network or something, along with HDE and some random guy

So yeah

0celo7

10:00 PM

Hmm, @SirCumference I have a mission for you

Sir Cumference

@0celo7 Huh?

0celo7

@SirCumference Sigidur Helgason dedicated his book to "Artie"

who is that

Sir Cumference

Is he choking?

0celo7

...what

Sir Cumference

If so he's an artiechoke

That's all I've got

0celo7

10:03 PM

...

it was a serious question

Oh my god

How would I know?

google

@SirCumference ?

@0celo7 lmgtfy.com/?q=Who+did+Sigidur+Helgason+dedicate+his+book+to

@HDE226868 Is the dispersion velocity of a star cluster simply the standard deviation of the star velocities in the cluster?

*velocity dispersion

HDE 226868

10:08 PM

@SirCumference No idea.

Sir Cumference

All right, thanks :/

HDE 226868

A quick Google yields this, which says

> Dispersion should here be interpreted as the standard deviation of the velocity components along the line of sight, even though the true velocity distribution in general is not gaussian

Sir Cumference

Awesome, thanks

0celo7

10:26 PM

Why didn't you google that yourself

You even gave me the LMGTFT earlier

ACuriousMind

10:45 PM

@BernardMeurer what do you need, my child?

Bernard Meurer

@ACuriousMind Hey :)

ACuriousMind

@BernardMeurer heyhey :)

Bernard Meurer

Is Heavy metal the main genre, with death metal, black metal, yadda yadda under it, or is Metal the main genre and heavy metal a subgenre together with black, death, prog...

ACuriousMind

@BernardMeurer nowadays, people tend to say just "Metal", but the overarching genre is "Heavy metal" originally

Bernard Meurer

@ACuriousMind Okay, great, then my Genre metadata style is correct :)

ACuriousMind

10:53 PM

@dmckee Well, there is gems from stack exchange but it's neither popular nor very good.

@BernardMeurer Was that seriously what you wrote "HALP" for? :p

Bernard Meurer

@ACuriousMind I'm very serious about my music metadata :p

ACuriousMind

I loathe people who get all hung up on what exact subcategory a certain type of music falls into :P

0celo7

@ACuriousMind Remember the finite intersection property?

ACuriousMind

@0celo7 I do

0celo7

@ACuriousMind They loathe you too

@ACuriousMind it showed up on my analysis homework and I proved it without help

I've come a long way since we first met

ACuriousMind

10:57 PM

Do you expect me to say I'm proud of you? :P

Bernard Meurer

@ACuriousMind I don't, I'm just grouping all my Metal-like music into Heavy Metal

0celo7

@ACuriousMind ...yes

Bernard Meurer

and wanted to know which name was best :)

ACuriousMind

@0celo7 I'm proud of you.

3

0celo7

You don't mean that

ACuriousMind

11:00 PM

Maybe I do

Maybe I don't

0celo7

You're a quantum duck

Danu

Why are there so many posts in the reopen queue?

ACuriousMind

Schrödinger's duck!

Bernard Meurer

@0celo7 Great moves Ethan

ACuriousMind

@Danu I suspect because someone who doesn't like us closing questions has discovered they can vote to reopen :P

Bernard Meurer

11:02 PM

Keep it up

DanielSank

@DavidZ I started a Google doc keeping track of posts which look like candidates for closure under the homework reason, but which I voted to close for other more well-defined reasons. Once there are enough to comprise a data set, I'll let you know.

0celo7

I'm proud of you

DanielSank

I'm proud of all of us.

0celo7

@DanielSank you're not proud of me

DanielSank

@0celo7 Sure I am. Way to go you!

0celo7

11:03 PM

...thanks

Danu

@ACuriousMind Is it peterh?

Bernard Meurer

@ACuriousMind Run my kernel

ACuriousMind

@Danu 1. Looking at the reopen queue, it seems about half of the questions in there were edited by their authors, so it's just coincidence. 2. Since reopen votes are anonymous until the question is reopened, I could not possibly tell.

0celo7

@ACuriousMind Will my QM prof know what the kernel of a linear operator is?

ACuriousMind

@BernardMeurer No

@0celo7 He should

0celo7

11:06 PM

@ACuriousMind He seems pretty mathematically savvy, so I'll trust you.

Bernard Meurer

@ACuriousMind Please

I need someone to test it

0celo7

Don't do it

last time he had me run shit, he took over my webcam

Bernard Meurer

Lies

0celo7

now he keeps a detailed log of what I do

Bernard Meurer

He likes midget porn

DanielSank

11:08 PM

@Danu Does it matter?

0celo7

@BernardMeurer not true

Danu

@DanielSank Not really. I just thought ACM knew from the way he phrased it, so I wanted to know.

0celo7

yes, ACM did seem to be hinting...

ACuriousMind

After going through the queue, I have seen that most questions were in there for edits. So it's just coincidence.

0celo7

11:27 PM

@ACuriousMind Since unit balls are always homeomorphic for any two norms on a finite-dim vec space, is it believable that all unit tangent bundles on a manifold are homeomorphic, or even diffeomorphic?

Maybe even isomorphic as smooth bundles?

(although diffeomorphic would be best)

ACuriousMind

@0celo7 What do you mean by "all unit tangent bundles"?

0celo7

@ACuriousMind $UM_g=\{(x,v)\in TM\mid g_x(v,v)=1\}$.

is $UM_g\approx UM_{g'}$

ACuriousMind

@0celo7 I'd call that a "sphere bundle"; are you talking pseudo-Riemannian or Riemannian metrics here?

DanielSank

Yeesh, I just reviewed three or four posts from the queue.

I'm exhausted now.

Reviewing is so much harder than everything else on this site.

0celo7

@ACuriousMind Riemannian, I've given up on GR

Sphere bundle isn't specific enough, there are other sphere bundles not of this form

I'm thinking it shouldn't be hard to write down the diff directly?

How do you diffeomorph between two Riemannian spheres? @ACuriousMind

ACuriousMind

11:37 PM

@0celo7 Then I don't know

0celo7

@ACuriousMind Then you don't know? You would know in the GR case?

ACuriousMind

@0celo7 In the case where we allow non-Riemannian metrics it would be obviously false since the "unit ball" of a Lorentzian metric is a hyperbola and definitely not an actual sphere.

0celo7

@ACuriousMind Ok, sure

@ACuriousMind So, different question. $V$ is a vector space, $|\cdot|_1$ and $|\cdot|_2$ are norms

ACuriousMind

@DanielSank I find giving good answers to be harder than reviewing :P

@0celo7 That's not a question ;)

vzn

in theory salon, 36 mins ago, by vzn

Richard Feynman and The Connection Machine / Hillis

0celo7

11:49 PM

@ACuriousMind got distracted by you-know-who, sorry

@ACuriousMind hmm, are norms smooth functions?

probably on $V-\{0\}$

ACuriousMind

@0celo7 I don't know you-know-who, unless Voldemort broke into your room

@0celo7 Smooth in what sense?

0celo7

@ACuriousMind there's one person who can distract me away from math

@ACuriousMind $C^\infty$

a norm is a function $V\to\Bbb R$

if we view $V$ as a manifold, is the norm smooth

ACuriousMind

@0celo7 How are you "viewing $V$ as a (smooth) manifold"?

0celo7

what

ACuriousMind

For instance, I do not know whether the standard Euclidean norm is "smooth" in the smooth structure of the exotic $\mathbb{R}^4$s

0celo7

11:52 PM

oh god

I'm looking at the tangent space?

So the charts are just isomorphisms to standard $\Bbb R^n$s

no exotic stuff please

ACuriousMind

what

0celo7

I'm so confused

ACuriousMind

My point is that given a norm $V\to\mathbb{R}$ you have not fixed a smooth structure on $V$, so asking whether the norm is smooth doesn't make much sense to me

0celo7

@ACuriousMind I want to map $UM_g$ to $UM_h$ by expanding each $g$ ball to each $h$ ball

expanding/shrinking

DanielSank

Awww, my favorite player was just knocked out of a Smash Bros. tournament.

Whatever, he's a winner in my heart.

ACuriousMind

11:55 PM

(btw, the norm on $\mathbb{R}$ (the absolute value) is obviously not smooth)

0celo7

I KNOW

that's why I said $V-\{0\}$

DanielSank

@DavidZ Perhaps. That's where I was going when I was writing out all the distributions. I worked out the distribution of $1/p$, but Wolfram Alpha didn't know how to do the integral I needed to get the mean.

ACuriousMind

@0celo7 Well, I'd say that (with or without the zero) carries no canonical smooth structure and hence the question isn't answerable

0celo7

;_;

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