The h Bar

@Danu Non-LMU people can't access that and can't even see the title of the paper

I'd be interested in a safari in SUSY-jungle

Wait, safaris aren't in jungles, are they? :/

@JohnRennie I find it pretty telling that your answer is both the only correct one and the only one with any math.

@G.Bergeron Yes. Although I usually find that that happens not simply because there are so many answers but because there are usually four or five answers saying the same thing in slightly different words.

@ACuriousMind Halp

How do I find the basis for the eigenspace associated with an eigenvalue of a given matrix?

"the" basis?

a basis

Don't be so german

3:12 PM

Well, you pick any basis of the eigenspace you like

$E(\lambda) = K(A-\lambda I)$ Right?

K being the kernel

I don't know what that equation is supposed to mean - what is $E$, what is $K$?

The eigenspace is simply the solution set to $(A - \lambda I) v = 0$.

E is the eigenspace associated with the eigenvalue

Or, if you wish, the kernel of $A-\lambda I$.

K is the kernel

3:14 PM

Ah, okay

AHA

So, yeah

One writes the kernel as $\ker(A-\lambda I)$ usually.

I had a matrix
3 0
8 -1

So I found that the spectrum is $\sigma=\{3,1\}$

Then I went on to calculate the eigenspaces for those

and doing $\ker(A-1I)$ gave me

|1 0| |x| = |0|
|0 1| |y| = |0|

(ignore the double equal for formatting reasons)

Now I don't know what to do to get to a basis

Is just the canonical base of $\mathbb R^2$?

uh

What exactly is that equation supposed to be?

Which equation

3:18 PM

The matrix on the l.h.s. is not $A-1 I$.

The who

What is the |1 0 | |x| = |0| thingy supposed to tell me?

Lol, okay, that did not get my message across

I'll learn how to do LaTeX matrixes

To determine the kernel, you have to solve $\begin{pmatrix} 2 & 0 \\ 8 & -2\end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}$.

Yeah! Exactly

$\begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix}$ is what you get if you do Gauss, right?

3:21 PM

The matrix has non-zero determinant, so the only solution is $x=0,y=0$.

No need to do Gauß

I suspect you botched the computation of the eigenvalues :P

Bah

All I did was $P(\lambda) = |A-\lambda I|$

$$|\begin{pmatrix} 3-\lambda & 0 \\ 8 & -1-\lambda \end{pmatrix}|$$

The eigenvalues are the roots of $(3-x)(-1-x) = -3 -3x +x +x^2 = x^2 -2x -3$

Why did you take it out of the neat little product form?

Well, you can read off $x = 3,x = -1$ from the first term

Wont the eigenvalues be 3 and -1?

Yeah

OH

GODDAMMIT

-1

3:24 PM

Yeah, so why did you take $A - 1I$ and not $A - (-1)I$ :)

JESUS CHRIST

No wonder the exercise was hard lol

It happens

3:39 PM

@BernardMeurer "lester"

3:54 PM

The quotes here are completely useless because you did not define what definition for "speed of light" you are talking about. As JohnRennie's answer shows, the local speed of light is constant for all observers, the coordinate speed is not. The answer does nothing to clear up this confusion. — ACuriousMind ♦ 1 min ago

yo @ACuriousMind you know how you can express the position vector $\mathbf r$ as spherical harmonics times circular-polarization unit vectors?

do you know off-hand any quick references for that stuff?

Though unlike most of Valev's answers it is not egregiously wrong

Also - this was pretty much what I wanted to comment just from seeing the title

@EmilioPisanty I'm afraid I don't know what you mean

@ACuriousMind never mind

too much trouble to explain

3:58 PM

@JohnRennie Yes, but it's not helpful either. As the question seems to be reasonably popular (thought not hot (yet)), I didn't want to leave the downvoted answers who pride themselves on citing Einstein & co. without an explanatory comment why they're being downvoted.

@EmilioPisanty Okay, I stay away from special function stuff as far as possible anyway ;)

@ACuriousMind well Valev's answer makes more sense, or perhaps less nonsense, than Duffield's. I mean, when you're being outpointed by one of the more notorious relativity denying crackpots of the last few decades that's got to smart. Yes?

4:24 PM

@ACuriousMind found it, if you're interested

$$\mathbf r = \sqrt{\frac{4\pi}{3}} r \sum_{q=-1}^{1} Y_{1q}(\hat{\mathbf r}) \hat{\mathbf e}_q^*$$

where $\hat{\mathbf e}_0=\hat{\mathbf e}_z$ and $\hat{\mathbf e}_\pm = \mp(\hat{\mathbf e}_x\pm i \hat{\mathbf e}_y)/\sqrt{2}$.

It's useful for taking matrix elements of the $\mathbf r$ operator between states of definite angular momentum.

but the normalization is (as always) a pain.

Hi, folks. :)

Afternoon (UK time)

Oh, it's night for me. Anyway, Good afternoon.

There's something I wanted to ask. Does general chat for physics stack mean people can talk other things here? (Though I'm least interested in wasting my time. Just curious).

4:39 PM

@AakashTomar we talk about all sorts of stuff. This morning there was a several hour long debate about philosophy and human morals (at least I think so, I wasn't really paying attention :-).

Haha, alright. Though, your conversation are pretty advanced for a high schooler. :)

Conversations*

@EmilioPisanty Ahh, I'm not sure I ever saw that formula before

@ACuriousMind well, now you know

;-)

fancy a dive into Gradshteyn & Ryzhik, btw?

@AakashTomar we get conversations at all levels. ACuriousMind and Emilio are currently discussing maths so advanced I can't understand a word of it :-) But we also chat about high school level science.

@JohnRennie Seriously? Spherical harmonics is too much?

=/

4:43 PM

@EmilioPisanty Not today, I have to go drink mulled wine at the Christmas market soon ;)

No, it's nice. For me, it's like. I'm in a weird country with a weird language, but I find the language to be really interesting. So I start learning the language, but I also start hanging around with the people of that place. When I hear them speak the stuff, soon, I'll start speaking it too.

@ACuriousMind fair enough

hah, found it

... unfortunately a liiiiiiitle more horrifying than I hoped for

@EmilioPisanty I was with you up to the spherical harmonics :-)

@DavidHerreroMartí: that is an uncharacteristic error from Jim. I'm sure that if you mention it in the chat room he'll immediately commit the physics equivalent of harakiri in shame. — John Rennie 1 min ago

@Jim You have been challenged.

ooh you troublemaker :-)

4:49 PM

@JohnRennie yeah, the Bessel function horror is the radial part of the integral =/

@AakashTomar a weird country with a weird language and very weird people :-)

No, I did not mean you're weird. I guess I'll provide a glossary or something. XD
Language = Theorems, ideas etc.
Country = Physics + Mathematics
People = You guys. And you're really smart, not weird. :P

Like what did that even mean. -_-

dear guys ,if
\[
\theta=4\pi rad
\]
means 2 times of circle, but I saw a
\[ \theta=1/2 rad
\] <-- how to imagine this?

Using your head, that's the best I personally can do.

hahaha

please help me, like no \[
\pi
\]

4:57 PM

Who flagged Hey-men's question? Flags are for seriously offensive posts.

What was offensive about that?

I thought it was done for things you can't understand , or for repetitive messages. Anyway, really sorry, I need to read the guidelines carefully.

Heymen, are you asking how to visualize an angle of 4pi radian?

And how do you unflag things? Sorry.

Yes, but there is no \[
\pi
\] in the second equation.

It's just like \[
1/2 rad
\]

so I don't know how to figure this angle in a circle

So you're asking how to construct an angle of 1/2 radian?

yes pretty much..

Okay, first, 180 degrees = Pi radian, right?

5:03 PM

@Hey-men-whatsup $\frac12 \:\mathrm{rad}$ is the angle such that the length of the arc it subtends on the unit circle is $1/2$.

The image isn't opening for me, really sorry.

@ACuriousMind log in to mathscinet; I think it should work

But, if it matters, 1/2 rad = 28.64 degrees. So you can use a protractor to construct that angle.

5:06 PM

@EmilioPisanty, thank you I see your point

@Hey-men-whatsup @Hey-men-whatsup this is how to visualise half a radian:

@JohnRennie really thank you, I appreciate it

If you have a circle of radius 1 then half a radian is the angle such that the length of the circle in that angle , the red line, has length a half.

Yes, it confused me because \[
\pi = 180^o
\]

while if there's no \pi what it would be

Why are you using \[ in your posts? If you want to typeset maths then use mathjax e.g. in this case $\pi=180^o$

Though note that MathJax won't render in this chat room unless you install some suitable script

5:13 PM

@Danu Uh, I have no idea how to sign in to mathscinet :P

I actually copy from here sharelatex.com/learn/Mathematical_expressions, like the shortest Latex codes, thiis the first time I use it

Q: MathJax basic tutorial and quick reference

@Hey-men-whatsup See:

1627

To see how any formula was written in any question or answer, including this one, right-click on the expression it and choose "Show Math As > TeX Commands". (When you do this, the '$' will not display. Make sure you add these. See the next point.) For inline formulas, enclose the formula in $......

somehow \[ needs enter (-_-") zzzz

@Kaumudi I want!

@DanielSank looks good doesn't it? :-)

I've just eaten this:

5:18 PM

$$ test... \Omega.. $$

wow... that's much better than [ ]

Pierogi with spinach and cheese, tossed in butter. Really good!

Jim

@ACuriousMind Wow, yeah. That was from a couple years ago. My terminology use has grown a bit more technically proficient.

The Pengest Munch Ep. 4: Dallas (Waterloo)

@JohnRennie Any comments on this guy?

►

It's, like... more British than making fun of Americans for not knowing what a cheeky Nando's is

oooooh, look, an American

@JohnRennie looks heavy, but delicious.

@DanielSank You've heard of cheeky Nando's?

5:30 PM

@EmilioPisanty 'fraid not.

@DanielSank pretty solid, yes. I knew I been eating after finishing that lot!

:D

In my (very limited) experience Eastern European food tends to be pretty solid but tasty. Polish smoked pork sausages are very, very good.

Do you ever polish off a meal without realizing your been eating?

I like sausage, in general.

Sausage, onions, apples --> sauté --> delicious

5:32 PM

@DanielSank go to any upmarket restaurant in London. You'll be served something that looks great, and to be fair tastes great, but is gone in two bites.

@JohnRennie oh, I see.

@EmilioPisanty perhaps unsurprisingly, I feel equally uninformed as before I read that.

@ACuriousMind Oh... Welp the thing I quoted was a mathscinet review of a paper

@DanielSank full roster here buzzfeed.com/alanwhite/…

So if you ain't got mathscinet... :P

there's a translation to American down at the bottom

5:34 PM

The first time I went to the US was to Michigan visiting Dow Corning. I had dinner in the hotel and ordered red eye perch. When it arrived I thought I'd died and gone to heaven. It was beautifully cooked and the plate was so loaded you couldn't have fitted anything more on it.

@JohnRennie yes we tend to have large portions at restaurants.

It's a blessing and a curse.

@DanielSank If I lived there I wouldn't be going to that restaurant for every meal :-)

@EmilioPisanty This is not British at all, is it?

Sounds/reads much more like Australian to me

@Danu that is 110% British English

@JohnRennie can verify

@EmilioPisanty Funny. Australians have very similar ways of changing words etc, then.

5:37 PM

@EmilioPisanty verified. Though note that that's in London and that isn't typical.

@JohnRennie yeah, it's probably only London, and only certain subsets of London at that

@JohnRennie indeed not

5:52 PM

@Kaumudi Well, to me "curry" is a context-dependent word.

Different people mean different things.

For example, Thai curry differs from most of the Indian styles.

6:08 PM

I don't think curry exists as a concept in India, apart possibly from when catering for western tourists. My father, who was based in India during WWII, told me that in the local language (he didn't say which language) the word just means sauce.

I think the word curry as understood by Brits was an invention of the Raj.

user246160

@JohnRennie Actually your father was right. Any dish with lots of spices and sauce/gravy and some herbs (optional) is called curry. There are over a 100 dishes that people call curry here :-P.

user246160

Even butter chicken is called chicken curry sometimes :-P

Secret

[Division by zero] Caption: No, this is way too trial and error, I have to calm down and think in terms of cosets when trying to test the associativity tomorrow...

user246160

BTW your father was a soldier ? @JohnRennie (asking due to the WW2 reference :))

Secret

6:18 PM

@TheStackExchange He was on the Northwest frontier. The British feared that the Russians would invade through Afghanistan (even though they were in theory our allies) and stationed troops there to prevent it.

In the event he spent most of his time fighting Pathans, who generally resented anyone who wasn't a Pathan. He had a great scar from where a Pathan stuck a knife in him. It was more dangerous than doing physics!!! :-)

Holy shit

user246160

@JohnRennie Wow. You seem to have an interesting family history :) ! Yeah, I know. Pathans are fighters by nature, and they don't like being messed with :P After the independence they even went on to form their own country (Pakistan) !

My father had only happy memories of the years he spent in India (even allowing for homicidal Pathans) and he learned lots of Indian cooking while he was there. My brother and I grew up eating Indian food.

Though the cooking my father learned was from the North West, which I think is mainly Punjabi syle.

The only place in India I've been was Pune in Maharastra and the food there was very different.

Ehm, I'm not the proudest of my family's war heritage :P

What were you doing in Pune?

user246160

@JohnRennie I bet you like Punjabi food more than Maharashtra's food :-P Punjabi cuisine is famous. Did you ever taste Bengali food ?

6:24 PM

@BernardMeurer Visiting Unilever Hindustan. That was when I worked for Unilever.

Ha, cool

@TheStackExchange I did, but to be fair I was more used to Punjabi food. If I had grown up eating Marathi food I'd probably feel differently.

You should write a book, "The adventures of the Rennies"

user246160

@BernardMeurer I agree. @JohnRennie do consider this one ^ :)

user246160

I would love to read :-P

6:27 PM

My mother was a bacteriologist. This is her

She's M. E. Brooks - Brooks was her maiden name.

Jesus, you're whole family is just awesome people

user246160

@JohnRennie The page isn't loading :(

user246160

"www.microbiologyresearch.org refused to connect."

That's odd, the link works for me ...

Works here too

user246160

6:30 PM

No idea why its not loading! Anyway I will check it later using another net connection :)

Try ncbi.nlm.nih.gov/pubmed/13804787

user246160

@JohnRennie Yes. That works!

user246160

Thanks

user246160

"Taxonomic studies of the genus Clostridium: Clostrididum bifermentans and C. sordellii."

user246160

Didn't understand a word of this ^...looks scary :P (well,except 2 words)

6:32 PM

My mother was working with a genus of bacteria called clostridia and they're absolutely awful. They cause gangrene and some of them can literally melt your flesh off the bone.

user246160

O_O

And she survived?

If I was a kid I'd be so afraid of my mom lol

Clostridium histolyticum

Clostridium histolyticum is a species of bacteria found in feces and the soil. It is a motile, gram-positive, facultative anaerobe. C. histolyticum is pathogenic in many species, including guinea pigs, mice, and rabbits, and humans. C. histolyticum has been shown to cause gas gangrene, often in association with other bacteria species. == History == In 1916, Weinberg and Séguin isolated this bacterium from patients with gas gangrene and called it Bacillus histolyticus. They discovered this bacteria was pathogenic for guinea pigs, mice, and rabbits, but less so for rats. Intramuscular injection of...

Ugh

> Intramuscular injection of culture caused extensive local tissue destruction, extrusion of a hemorrhagic muscle pulp, splitting of the skin, denudation of the bone, and sometimes autoamputation.

Nice

For some reason putting it on google images eventually yields a broken penis

user246160

I'll have nightmares tonight O_O :P

user246160

6:35 PM

@BernardMeurer what !

user246160

bacteria does look like that, actually :-P

@TheStackExchange Searh the name on google images and scroll

user246160

@BernardMeurer "broken penis" is too much of an exaggeration :P

@TheStackExchange No, no. I wasn't joking, there's an actual broken penis

user246160

6:41 PM

@BernardMeurer Ok I saw it. Now I want to unsee!

LOL

I thought it looked quite interesting

user246160

@BernardMeurer yikes!

user246160

yuck yuck yuck :P

The things you find on the Internet ...

Anyhow, now I'm traumatised by that Google image search I'm going to slump into my armchair and drink a beer to recover. I'll see everyone tomorrow.

Hahahaha, my bad John

See you tomorrow ;)

user246160

6:49 PM

@JohnRennie Bye !

user246160

@BernardMeurer I'm sure to have nightmares tonight! Bye buddy :-D

7:15 PM

@BernardMeurer: I need help. Clinical help that is. I just bought this for no better reason than I thought it looked fun :-) Dell Inspiron 17R-5720

7:30 PM

Hi, @BernardMeurer.

You should be playing Metroid II.

Not wasting your time here.

vzn

Listening to the Heavens: The Discovery of Gravitational Waves Proved Einstein Right / MIT tech review, brought to you by ADI

Shing

I was playing Tyranny.

a great game

@JohnRennie Oh my god, you need treatment

@DanielSank Doing algebra exercises

Exam in a week

@JohnRennie You bought a laptop because it "looked fun"?

2

@DanielSank He's nuts

7:35 PM

@BernardMeurer I knew that.

Dude, do you know how badly I want to play Smash Bros with you?

I'm going to get rekd so bad

But it'll be fun :P

I gotta visit again

Just made an account with Mouser.

I'm a real engineer now.

Bloody physicists stealing my job

Mouser is awesome

Take that.

I bought this

Oh nice!

I'm still dating the ColdFire MCU DevKit

7:43 PM

do it

for messing with 68000 architecture

I'm saving :)

Why don't you buy an FPGA and program an electronic instrument?

That's also an idea

Wouldn't know which brand to get though

Xilinx, Altera,...

Doesn't matter, d00d

Just get a cheapo dev board.

adafruit.com/product/451

I thought of this for a while

7:48 PM

@DanielSank These are ex business laptops that have their disks removed by the company's IT guys when the laptops are sold on. Because they have no hard disk they go for ridiculously small amounts of mony. £82/$103 for a pretty powerful laptop with a 17 inch screen.

I bought one for my niece a couple of months ago, and while I was setting it I up I thought this is a really nice laptop I wish I'd bought myself one. Now I have :-)

@JohnRennie where do you find these?

@EmilioPisanty Ebay

just ebay for laptop with no hard drive?

@EmilioPisanty eBay

@BernardMeurer yeah, but there's many a laptop on ebay ;-)

7:50 PM

@EmilioPisanty Search dell latptop, if you know models it helps, sort by price

@BernardMeurer huh

I normally don't trust the bottom of that sort

but maybe I should reconsider

In this case I wanted a laptop with a 17" screen, and there aren't many of them. My niece wanted the big screen laptop to watch blurays on.

Intel Core i5-3210M, though

@EmilioPisanty You need to know what you're buying. I only buy Dells and I know the Dell range very well. If you're looking for a cheap laptop I can advise and maybe point you to likely looking examples on ebay.

@JohnRennie nah, I'm mighty happy with my jumping tiger

7:52 PM

@EmilioPisanty cpubenchmark.net/cpu.php?cpu=Intel+Core+i5-3210M+%40+2.50GHz

HP spectre x360 15

That's still a mighty powerful CPU.

but I might consider taking one of these as a project in a few months

CPU power hasn't advanced that much in the last few years. The high CPU benchmarks have come from squeezing lots of cores on a chip, but of course you only get that power in apps that can be parallelised.

John's right, the only improvements we've been seeing are power dissipation/energy consumption

7:55 PM

If you look at the single thread speeds then even the very latest fastest ridiculoulsy expensive CPUs are barely twice the speed of the i5 in that $100 laptop!

@JohnRennie indeed. but if I get one of those then I'll probably be looking to make it into a desktop replacement where I can run beefier (possibly parallelized) Mathematica and other work computations

@EmilioPisanty I recently specced up a workstation for a friend who wanted to do finite element work. It had twin 22 core E7s. Yes, that's 44 CPUs :-)

The finite element stuff works a treat on multiple core workstations because it's very easily parallelised.

@JohnRennie yeah, OK, not quite that much beef on a single machine

if it needs that much muscle then it probably needs a cluster

@EmilioPisanty Also when you're running it you won't need the heating on :-)

@JohnRennie I imagine

but I'm moving in a few weeks to a city where the problem is heat instead of heating ;-)

7:59 PM

@JohnRennie Have you looked into using GPUs?

@G.Bergeron My friend works in the nuclear power industry and they use approved software from well known suppliers. Software bugs matter when you're designing power stations :-) Anyhow I don't know if the finite element software supports GPU offloading. I suspect not.

Bernardo messes with GPU offloading using CUDA I think.

@JohnRennie Ah, yeah. If he's not rolling up his own libraries it is gonna be a major hassle

I do, yeah

Jaime Gallego

@JohnRennie Tell that to FirstEnergy during the 2003 blackout

In particular I've been messing with OpenCV and cuFFT

8:02 PM

The 44 (!) CPU workstation was only about £6k. I mean yes that's a lot of money, but then it's a storming workstation and anyway the nuclear power guys have large budgets.

I want to use what's being done for deep learning to do other stuff: My brother works on Theano and you can do a lot of stuff without using CUDA directly

@JaimeGallego see, they should have got my friend to work for them :-)

Mass parallelization helps so much though, it's almost silly

histogram matching for example, it's so slow on the CPU but just flies on the GPU

I wish I had a Jetson TX1 :P

@BernardMeurer Yes! The things I want to do would require a lot of computing ressources and I wouldn't have the kind of money to enable that without GPUs. But I am still learning to do all that

Well, not everything is better on a GPU though

Computing factorials for example

8:05 PM

To be fair, even the top end GPUs are pretty expensive these days. Setting up a really fast number cruncher is still going to cost a bit.

Say you want $n!$ for $n>10^9$

@JohnRennie Thanks for writing that, btw. That's a great resource for the future.

The memory complexity grows dangerously with parallelization, and as the complexity is already high for such numbers when you implement the parallelization the memory constraints do more damage than good. You're active memory regions get split on GDDR and your ordinary RAM and sheesh

^ Literally the only thing I know about in computing, and I just know a bit

@BernardMeurer I know, but what I want to do is.

@EmilioPisanty It was great timing. I had been annoyed by the comments about the velocity of light in my answer to Is Einstein's theory really challenged by the recent paper in news?

And I was particularly annoyed to be downvoted by someone who appears proud of his ignorance of differential geometry.

So I was really pleased when an opportunity came up to write the definitive answer on what the speed of light means.

8:10 PM

@JohnRennie well, I've been annoyed by misdigested Einstein quotes from that paper (and related ones) on this site for a pretty long time now.

This one was also quite welcome (I'd been wanting to write about that for over a year), but it's waaaaay nerdier.

That is a great answer :-)

@JohnRennie thanks :-)

@JohnRennie Yeah but I can buy a good consumer model and put that on a desktop thingy to have some kind of basic computing server that still packs quite a punch

@G.Bergeron very true.

that ring-of-fire figure really came out well

8:13 PM

Do I detect the hand of Mathematica there? :-)

Much colors

@EmilioPisanty Is there a lot of q-Pochhammer in there?

@JohnRennie yes, you do

@G.Bergeron ah, good question. Mostly not, but "definitively not" is a pretty strong statement

that's a Jacobi $\theta_3$ function, $\theta_3(z,q)=1+2\sum_{n=0}^\infty q^{n^2}\cos(2nz)$.

you tell me if it's got Pochhammers in it or not

@G.Bergeron but theorists who think that everything can always be analytically continued everywhere (modulo branch cuts and whatnot) would do well to pay attention to that example ;-).

@EmilioPisanty There is, but only when evaluated at a given $z$

@EmilioPisanty But this usually appears in q-deformed whatever where a value of $q$ outside of the unit circle is not expected

whatwhatwhat

Hello everyone!

8:21 PM

@G.Bergeron well, here you have a case where the only physically relevant case is right on the unit circle at $|q|=1$.

@EmilioPisanty It brings good/bad memories: the only problem I solved numerically was when after solving exactly for a correlation function expressed as an integral, I wanted to plot it in some parameter space... Imagine asking mathematica to NIntegrate a page worth of product of expression like the one you posted

I've never been too sure of what all that $q$-deformed stuff is, though.

@EmilioPisanty Exactly, q is usually in or on the unit circle

@EmilioPisanty It often comes because the dynamical algebra (really a Hopf algebra) gets deformed and you don't have many possibility doing so

@G.Bergeron you use $q$s on the unit circle in cases where it is a natural boundary?

For instance, in spin chains when you introduce anisotropy in the isotropic case, you get an anisotropy parameter that leads to q-everything

@EmilioPisanty what do you mean?

@EmilioPisanty Quantization of classical mechanics into QM is a deformation of the algebra of observable on phase space. The phase space becomes a non-commutative space, hence why it kind of disappears from the picture and points on it are no longer meaningful.

The q-things in model is the same procedure, but applied to the symmetry algebra. After that the Lie manifold also disappears, but the important structure we need to talk about symmetries in physical models is really a Hopf algebra, not necessarily a Lie group

It is also the same deformation procedure that is involved in the non-commutative geometry approach to quantum gravity

In this case the deformation is applied to the $C^*$ algebra of the function on spacetime

8:30 PM

@G.Bergeron what I mean is that for the $\theta_3$ case the $|q|=1$ unit circle boundary is not just a special case - it is the absolute maximal extent to which you can analytically extend the function, and you can prove that it blows up to infinity as $|q|\to1^-$ regardless of on which direction you approach the boundary

mathematicians are only interested in $|q|<1$, and whenever mathematicians say that the default is to assume that those are the only interesting cases, but that is not the case here.

If you've got other examples like this, though, I'm definitely interested

@EmilioPisanty I have worked on a bunch of systems that are obtained as a $q\to -1$ limit.

@G.Bergeron yeah, but is $|q|$ a natural boundary in those systems?

It leads to particles obeying parastatistics.

@EmilioPisanty What do you mean? That $|q| > 1$ be meaningless in those system?

Take the XXZ model for spin chain

@G.Bergeron A natural boundary is a concept in complex analysis

it is the boundary of a domain, with the property that the function of interest diverges to infinity whenever you approach the boundary

Ah ok, I see what you mean

8:43 PM

and it is actually surprisingly generic.

Take, for example, any series you want, with convergence radius 1

To me that just the maximal analytic domain

@G.Bergeron sure

Not many people I've talked to about this, even pretty strong theorists, are aware that 'maximal analytic domain' can be less than $\mathbb C$

either way

if you know examples of physical relevance where the important cases have a parameter sitting at the boundary of the maximal analytic domain, then I'm interested