The h Bar

Secret

16:03

9 mins ago, by John Rennie

@MichaelHarding hello?

uh what, now we are having the opposite on what I have been rambling about in the last 3 days...

Semiclassical

echo echo echo

Secret

I am starting to believe h bar is weirder than quantum mechanics and GR combined

Semiclassical

well, the hbar is currently full of people

so hbar != 0 and indeed hbar >>1

Secret

yeah. which sadly often means I need to go to sleep. Grr timezones...

Semiclassical

therefore we're in a highly nonclassical regime and we should expect weirdness :P

Secret

16:06

> We expect the tunneling probability will not be adequately explained by the WKB semiclassical approximation

Semiclassical

lol

strongly coupled

Secret

ok I am off for the night

Semiclassical

night

Secret

try to make a higgs boson in the dynamics lol

Eric Silva

wow circuits just hurt my brain

Semiclassical

16:08

circuits are great man

as long as they involve linear elements at least

once you start including nonlinear stuff (e.g. a diode) then things sorta suck

Eric Silva

my prof just started drawing a bunch of circuits and idk i guess ill just sit here and not understand

Semiclassical

lol

Eric Silva

lol im so much worse at physics than i am at math rip

Semiclassical

context?

Eric Silva

i am just constantly a little confused in physics

Semiclassical

16:12

yeah

it's hard to start midway in

Eric Silva

yeah i kind of regret not trying to learn them seriously in tandem

Anonymous

@EricSilva Are you dealing with diodes and transistors?

Eric Silva

idk what those are so i guess not but tbh i could be wrong

Semiclassical

main thing is just this. with a resistor, the current through it is proportional to the voltage across it

Anonymous

Other than those diabolic stuff circuit analysis is pretty easy if you know the basic techniques :p

Semiclassical

16:17

and similarly, the charge of a capacitor is proportional to the voltage across it

additionally, a resistor and a (textbook) capacitor are bidirectional: to reverse the current, you apply the same voltage in the opposite sense

a diode, though, responds differently to voltages applied in one direction vs. the other

Anonymous

Fourier and Laplace transforms are also pretty useful in complicated circuits

Eric Silva

hmmk

Semiclassical

so it's easy to put current in one direction through a diode, but it won't allow the other

not without a lot more voltage than you'd expect, anyways

main thing is that the current os

Anonymous

@Semiclassical That's an underestimation considering the huge variety of differences that can occur in diodes. Mainly when you're dealing with the teeny-weeny diode currents

Anonymous

But in basic circuit classes they usually neglect the inner workings of the diode

Semiclassical

16:20

right

Anonymous

And treat it as a black box

Semiclassical

main point is that a diode isn't a linear circuit element

the response isn't proportional to the applied load

resistors/capacitors/inductors are, by contrast

which makes things easy since then the ODEs you get are linear systems with constant coefficients

0celo7

@EricSilva a proper physicist doesn’t understand that either

Circuits are for engineers

Semiclassical

ehh, depends on what one means by that

in terms of principles like energy conservation, charge conservation, etc

Eric Silva

im neither a proper physicist nor am i an engineer

Semiclassical

16:22

a physicist definitely knows what's up

but when it comes to how the individual elements work, then yeah

Balarka Sen

someone thought "ben sucks" was a bannable offense. sigh

@Semiclassical @Eric so I read that article

Semiclassical

i saw

i think it's pretty stupid

Balarka Sen

reading it linearly put me to sleep, so I read it from bottom to top

and I couldn't see anything interesting it says

Semiclassical

main point is just that it's a UChicago prof speaking in defense of Milo

Balarka Sen

yeah I got that

That explains a lot

Eric Silva

16:24

she never really says anything interesting tbh she just gets mad and says words and none of it really amounts to anything

Semiclassical

there was also a blog post which was a bit more colorful

0celo7

@EricSilva perfect description of a physicist

John Rennie

Drama in Chester!

Balarka Sen

A lot of Milo fans says "mumble mumble Milo points you out that everyone's touchy about religion mumble mumble" and I'm like, dude you know that the issue is that a major part of the current right-wing movement in US is about glorifying Christianity, right?

Semiclassical

@BalarkaSen glorifying a specific version of Christianity at that

Balarka Sen

16:27

Catholicism, fair

0celo7

@BalarkaSen feels bad when you’re an atheist republican so the other Republicans think you’re evil

Semiclassical

uh

0celo7

@BalarkaSen what?

Semiclassical

I didn't have catholicism in mind, no

0celo7

You clearly do not understand American politics if you think Catholics are the problem.

Eric Silva

16:28

the person who wrote the blog post he read is a staunch catholic

Balarka Sen

I do not think it's a problem

Semiclassical

oh, fair

Balarka Sen

what Eric said

Semiclassical

usually the touchstone is protestant evangelical Christianity

Eric Silva

but as someone who grew up in a catholic house other christians fuckin hate catholics and i dont know enough about christianity to understand why (considering i am not and have never been one)

Balarka Sen

16:29

@Semiclassical Ah

Semiclassical

something something the Pope = Illuminati?

idgi really

Eric Silva

idk the protestant revolution was something about catholicism being evil and the pope being evil so youre probably right

so i guess all the branches that were born out of the protestant revolution carry within them this nascent hatred of catholicism which birthed them maybe

0celo7

@EricSilva same

@EricSilva 500 Years ago...

Semiclassical

i think it also goes to the extent for which protestant theology hinges upon an individual faith relationship with Christ

0celo7

I’ve always thought Catholics were the chillest

Balarka Sen

16:32

I know about the catholics vs protestant thing but only superifically

Eric Silva

i think there's also something about other christians thinking catholics like worship saints

0celo7

It’s the crazy baptists you see walking around with bibles

Semiclassical

and thus views an institution like the Catholic Church as irrelevant at best and idolatrous at worst

@0celo7 or Jehovah's Witnesses

I've seen them around campus

0celo7

@Semiclassical don’t see those too much in the south

Semiclassical

@0celo7 nah, Unitarians are the chillest

0celo7

16:33

That’s not even a real thing

A religion has to be around for 500 years, otherwise it’s a fad

Like Scientology and Mormonism

bolbteppa

If in the EM path integral, the $A^{\mu}$ are scalars, and correlation functions come from $\partial_{J_x} \partial_{J_y} Z(J) = <A(x)A(y)>$, what does $<0|T\{ A(x)A(y) \} |0>$ even mean

Balarka Sen

what about mormons

oh you beat me to it

Eric Silva

@BalarkaSen i thought mormons were a thing from a musical

(that's a joke btw)

Balarka Sen

lol

Semiclassical

eh, Jehovah's Witnesses are more recent than Unitarianism

Slereah

16:35

Are there any Unitarian operators

Eric Silva

the only religion i take seriously is totemic religion

Slereah

Tengriism is the one true religion

Semiclassical

the joke from the simpsons i always liked was bart simpson and todd flanders playing a video game where you had to shoot bibles at people to make them christian

Eric Silva

@Semiclassical it's not just a game that's how it works in real life

bolbteppa

You can't even define $<0|T\{A(x)A(y)\}|0>$ if you start from the path integral, need to work with $<A(x)A(y)> := \int \mathcal{D}A A(x)A(y) e^{iS}$ right

Semiclassical

16:37

Todd: Keep firing. Convert the heathens.
Bart: Got him!
Todd: No, you just winged him. Now he’s a Unitarian.

0celo7

@bolbteppa whom are you talking to?

Balarka Sen

i only believe in the religion of Karl Marx

bolbteppa

@0celo7 you, you read Zee

Balarka Sen

Das Kapital is my religious textbook

even though i have not read it

Eric Silva

@BalarkaSen is the religion of marx that religion itself is a result of material conditions?

and capital accumulation

dude read kapital it's good lit

Balarka Sen

16:38

I have read the reader's digest

Communist Manifesto

Eric Silva

read the eighteenth brumaire

Slereah

I think @0celo7 doesn't believe in path integrls

bolbteppa

What the hell, that is shocking

Balarka Sen

oh yeah you told me to read that before

Eric Silva

literally every other sentence is top tier

Semiclassical

16:39

tbh path integrals do seem like black magic to me

Slereah

They mostly are

Some are well defined

But only some

Balarka Sen

what is a path integral

is it a functional over the loopspace or what

Semiclassical

The physicist's take on Clarke's 3rd law

Slereah

It's a integral over function spaces

Balarka Sen

what measure

Slereah

16:42

Depends

Usually Gaussian measure

Eric Silva

measures infinite dim spook me

bolbteppa

Oh man, how do you even define a particle from a path integral perspective

You think you're doing great until you realize you were using canonical quantization implicitly half the time

Slereah

You just have boundary condition measurements

ie you measure a particle at point x, you compute the probability of finding it in some open set at a later time

bolbteppa

'A photon is just $J^{\nu}$ at $y'$ in $<A(x)A(y)> = \mathcal{Z}(0)^{-1} \dfrac{\delta }{i \delta J^{\rho}(x)} \dfrac{\delta }{i \delta J^{\sigma}(y)} \mathcal{M} \exp [ \frac{i}{2} \int \, d^4 x' \, d^4 y' \, J^{\mu}(x') \Delta^F_{\mu \nu}(x'-y')J^{\nu}(y') ]$ :p'

Slereah

Same with fields except you use fields at a time t

0celo7

16:49

The epistemology of QFT is fucked, honestly.

bolbteppa

So there is none of this $A(x)|0>$ stuff apparently, or there is even though $A$ is a scalar, madness

Slereah

although of course almost all QFT uses no boundary conditions

Except LFT

bolbteppa

Seems like you can't ignore canonical quantization and just use path integrals I guess

Slereah

Oh also there's that weird alternative

bolbteppa

I just view the path integral as the Green function of the Schroedinger equation for now

What alternative

Slereah

16:53

Which is half path integral half canonical

bolbteppa

Hmm

What is that

Slereah

Where you use $$\langle \Psi, \Phi \rangle = \int D\phi \Psi^* (\phi) \Phi(\phi)$$

Both of these agree for the vacuum since the vacuum is just 1

bolbteppa

The Schroedinger functional formalism I think

I think that is basically just the Schroedinger equation where you throw away position vectors and then view the path integral as it's green function

'but, like, dude, the path integral is a completely independent perspective, man, where arrows rotate and then you describe the world'

Slereah

Wavefunctional

bolbteppa

Even Srednicki starts from canonical quantization and pulls the path integral out of nowhere only for correlation functions

Slereah

17:00

the path integral is the Hilbert inner product

you can do correlation functions with canonical formalism but it is a huge bitch

bolbteppa

Yeah it's really just not worth ignoring LSZ and path integrals, you get everything in 1 go so nice

Slereah

I'm not 100% sure what the relation between path integral and wavefunctional formalism is

Since you have like $$\int \mathcal D\phi \Psi^*(\phi, t) \Phi(\phi, t) \approx \int^{\phi_f}_{\phi_i} \mathcal D \phi$$

there's something like that but I'm not sure how it relates exactly

bolbteppa

Hatfield does it, treats the Schrodinger equation as an equation where the Hamiltonian is the e.g. KG Hamiltonian in terms of fields, $\int d^3 x \pi^2 + \dots$ and then just derives the Green function for Schroedinger with this insane Hamiltonian, in other words he actually derives the path integral without just saying what it is

Slereah

the boundary conditions in the path integral formalism relates to the states in the wavefunctional one

Oh plenty of people derive the path integral

bolbteppa

Yeah I remember him mentioning boundary conditions

Slereah

17:06

I'm pretty sick of seeing the derivation really

bolbteppa

It's not the $|q>$ derivation (I hate that one)

ACuriousMind

Finally! My internet connection was broken since Thursday, now it's finally working again

Slereah

Hurray

0celo7

I thought you died

Slereah

RIP

0celo7

17:07

My emotional reaction to that realization will be secret

Slereah

(he cried a lot)

0celo7

Tears of joy

ACuriousMind

@0celo7 If you dance on my grave I will come back to haunt you

Slereah

the simpsons evil homer dancing.wmv

►

btw, you know who has the actual path integral solution with boundaries?

Rovelli.

it's kind of a weird solution

Balarka Sen

@0celo7 Not Nice

Slereah

17:12

$$\exp[\frac{i}{\hbar} \int \frac{d^3 k}{(2\pi)^3} \frac{\omega}{2\sin(\omega T)} ((\varphi_a^2(k) + \varphi_b^2(k)) \cos (\omega T) - 2 \bar \varphi_a(k) \varphi_b(k)) \prod_k [\sqrt{\frac{\omega}{2 \pi i \hbar \sin(\omega T)}}]$$

bolbteppa

I have never even seen how you get the path integral for EM from the Schroedinger equation

Balarka Sen

@ACuriousMind also Not Nice

ACuriousMind

@BalarkaSen I might be a Nice ghost

Slereah

Where $\phi_a$ and $\phi_b$ are the (fourier transform of) boundary conditions

Balarka Sen

threatening to come back to haunt people from the grave is not acceptable

Slereah

17:12

@ACuriousMind A FP ghost

bolbteppa

It's so confusing, the answer is so simple, just put $\mathcal{L}$ in the exponent, and remember quadratic Lagrangian means the derivation will work, so there...

Slereah

@bolbteppa wot

ACuriousMind

@Slereah Ah, but then I'd decouple from all physical processes, which is boring :P

bolbteppa

Where does the path integral come from, either you wave your hands and talk about phases like Peskin, or you derive it as the Green function to Schroedinger right

Slereah

one thing I do wonder is if the same effect from non-relativistic path integrals affect the QFT ones

Is the class of functions non-differentiable anywhere

wrt $t$ only maybe?

I dunno

bolbteppa

17:15

Zee does something interesting, discretizing the non-rel Lagrangian so it looks like the KG action, after you did the non-rel $|q>...$ path integral, which sort of covers the EM action too

Slereah

Doesn't Feynmann Hibbs do the EM path integral?

Except weird

Where everything is Fourier transformed

bolbteppa

I would be shocked if he does anything but derive it with phases and arrows then just saying you put $\mathcal{L}_{QED}$ in the exponent, will check sometime

(Side-note - what is the Schroedinger equation for the Double-Slit experiment? Apparently it doesn't exist)

0celo7

@BalarkaSen flag it

@ACuriousMind you’d probably get grossed out if you follow me around everywhere

Balarka Sen

yeah 0celo7 has DiarreahG

ACuriousMind

@0celo7 I could haunt you part-time

Rearrange the order of the books on your shelves, change your passwords, that sort of thing

Leave physics "proofs" in the margins of your functional analysis texts

Balarka Sen

17:21

lmao

0celo7

Rearranging the books is evil

I have major OCD when it comes to my bookshelf

Slereah

@bolbteppa I think it's just free particle + an infinite potentials for the barrier

bolbteppa

I would have thought so, apparently it's not, I have no idea how to model it and vague googling told me it doesn't exist and papers trying to model it and I gave up

0celo7

@BalarkaSen my poop is in 3 states of matter

2

Sometimes 4 but only after lots of peppers

Slereah

I hope it's not a Bose-Einstein condensate

it would crawl up the toilets

Balarka Sen

17:33

maybe it would

we need to get 0celo7 to poop at low temperature environment

for science

Anonymous

And then high temperature too

Anonymous

To ionize it to plasma

Balarka Sen

i have been telling him "go to gulag" for a long time

he thought i was doing it for political reasons

but its really because of science

Slereah

I got the Friedlander btw

let's look up the integration by part

John Rennie

@BalarkaSen just out of curiousity, who is the Ben that you think sucks?

Balarka Sen

17:43

Shapiro

bolbteppa

The cool kids philosopher

Balarka Sen

that was a good article

bolbteppa

static.currentaffairs.org/2017/12/the-cool-kids-philosopher

Abcd

(@JohnRennie Do you know the mathjax code for single bond? )

John Rennie

@BalarkaSen you got suspended for saying Ben Shapiro sucks? Obviously there were a lot of republican supporters in the room at the time.

Balarka Sen

17:45

@JohnRennie Yup, seems so

Abcd

Using - gives it as a superscript.

Balarka Sen

But alternatively it could just be a troll

like 70% of the flags in SE

John Rennie

@Abcd using the chemistry module for MathJax?

Abcd

yes, I am typing a question on Chemistry.SE.

John Rennie

I don't think there is any support for chemical diagrams in regular MathJax

bolbteppa

17:47

"To see how operators naturally emerge in a formalism defined entirely without operators",
hmm, Kaku seems to do it...

Abcd

Not able to make single bond in CH2-OH......

@JohnRennie wait, now "-" works finally.

John Rennie

@Abcd see this article

You need \bond

Abcd

How to put a bracket below an atom?

Like a label...

John Rennie

No idea

There's a big MathJax help document somewhere ...

Aha it's here

DanielSank

Hi, everybody

@JohnRennie fix my laptop plz.

John Rennie

17:51

@DanielSank what's up with it?

bolbteppa

'the difference between Lagrangian and Hamiltonian formalisms is a Gaussian integral'

John Rennie

@0celo7 your poop is non-Newtonian. I wonder if Newton's poop was Newtonian ...

3

DanielSank

@JohnRennie It has broken Windows 8.

You know, that patch they released that makes the updater run all the time and hog the CPU.

John Rennie

@Abcd there's a whole load of stuff about putting symbols under letters here

Anonymous

Windows 8 is broken (by default) :p

Captain Bohemian

17:55

@bolbteppa what is Gaussian integral? I also have read the term Gaussian transformation but don't know what it is.

Abcd

6

Q: How are orbitals arranged in an atom?

I'm really confused about the ideas of orbitals, shell, subshell and most importantly how are they arranged in an atom? According to my knowledge orbitals are region having highest probability of finding electron.When I saw this video, I was more confused than ever. Lets say for a second that I ...

-1

Q: Structure of Atom?

I'm really confused about the ideas of orbitals, shell, subshell and most importantly how are they arranged in an atom? According to my knowledge orbitals are region having highest probability of finding electron.When I saw this video, I was more confused than ever. Lets say for a second that I ...

orbitals atoms atomic-structure

Look how the same question is received differently on two sites. Doesn't this clearly show how badly Chemistry.SE works?

Anonymous

@CaptainBohemian Why not just search on the net...

Anonymous

Gaussian integral is a pretty common integral

Slereah

Yeah

John Rennie

@DanielSank if you wish to stay sane copy your data off, reformat and install a new squeaky clean version of Windows 10 then copy your data back. Your Windows key will cover you for Windows 10 so you don't need to pay anything. Even the install files can be downloaded from Microsoft.

Abcd

17:57

@JohnRennie thanks.

Slereah

There's a generic formula for gaussian integrals

Captain Bohemian

@Blue do you mean that Gaussian distribution?

Slereah

Like $$\int x^n e^{i(ax^2 + bx + c)}$$

bolbteppa

@CaptainBohemian $\int_{-\infty}^{\infty} dx e^{-x^2} = \sqrt{\pi}$

If that's right

Anonymous

Gaussian integral

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line. It is named after the German mathematician Carl Friedrich Gauss. The integral is: ∫ − ∞ ∞ e − x 2 d x = π ...

Slereah

17:58

It's useful to have for path integrals

John Rennie

@DanielSank ask any of the numerous chat room members who I've talked through a Windows 10 installation. It's by far the best solution.

Captain Bohemian

then I have learnt that in quantum mechanics book.

John Rennie

@blue back me up here!

Slereah

\begin{equation}
\int_\infty^\infty e^{\alpha(ax^2 + bx)}\ dx = \sqrt{-\frac{\pi}{\alpha a}} e^{-\frac{\alpha b^2}{4 a}} \nonumber
\end{equation}

\begin{equation}
\int_\infty^\infty x\ e^{\alpha(ax^2 + bx)}\ dx = - \frac{ b}{4 a} \sqrt{-\frac{\alpha \pi}{ a}} e^{-\frac{\alpha b^2}{4 a}}\nonumber
\end{equation}

\begin{equation}
\int_\infty^\infty x^2 \ e^{\alpha(ax^2 + bx)}\ dx = (\frac{\alpha b^2}{4a^2} - \frac{1}{2a} )\sqrt{-\frac{\alpha \pi}{ a}} e^{-\frac{\alpha b^2}{4 a}}\nonumber
\end{equation}

Useful to have for path integrals

bolbteppa

His exact quote:
"By performing the functional integral over $\mathcal{D}p$, we can go back and forth between the Lagrangian and Hamiltonian formalisms. In the path integral formalism, the relationship between the Lagrangian and the Hamiltonian formalism is no mystery, but simply the byproduct of performing an additional functional integration over momentum."
I wonder if the Legendre transform is legit related to this...

Anonymous

18:00

@JohnRennie Ah, yeah @DanielSank. I back up John as far as the recommendation to install Windows 10 goes. Dump Windows 8 XD

Emilio Pisanty

11

Q: We are discontinuing support for identification questions

Since its very inception this site has struggled with the problem of identification questions and their controversial nature. Over the years these questions have become more and more of a quality and moderation issue and the community grew more and more weary of them and the work they generate as...

discussion featured scope identify

↑ well, this is new

Slereah

@bolbteppa Well the Legendre transform is gonna be the classical limit I guess

bolbteppa

'and now we perform the classical limit of a contact transformation on a jet bundle'

John Rennie

@EmilioPisanty there was some discussion on the SciFi SE about taking the SF film ID questions.

Emilio Pisanty

@JohnRennie this, no? yeah, that's where I saw it

don't ask me why I was there

bolbteppa

18:02

I can almost deny the existence of the Heisenberg rep and re-define it in terms of path integrals...

Slereah

Oh no

Not the jet bundle again

John Rennie

@EmilioPisanty we'll convert you to a SciFi nerd one day :-)

Slereah

Well if you have path integrals, you don't need anything from the Heisenberg rep

John Rennie

At least one of our moderators has a high rep on the SF SE

Slereah

Although it is still done a lot because path integrals and canonical quantization each have their own benefits

Emilio Pisanty

18:04

@JohnRennie unlikely

bolbteppa

Hmm, but in Compton scattering you do $<p',k'|p,k> = <0|a(k')b(p')a^{\dagger}(k)b^{\dagger}(p)|0>$ and then use LSZ and pah integrals and you get the monster, I'm hoping to re-define fields via path integrals and then get LSZ from it just to see if you can do it

Emilio Pisanty

I was here mostly to complain aloud that it's wildly unfair that Stokes gets two concepts named "anti-Stokes"

bolbteppa

You need those stupid $|p,k>$ vectors

Emilio Pisanty

Stokes line

A Stokes line is the radiation of particular wavelengths present in the line spectra associated with fluorescence and the Raman scattering. Stokes lines are of longer wavelength than that of the exciting radiation responsible for the fluorescence or Raman effect. Stokes lines are named after Sir George Gabriel Stokes. The energy of the scattered radiation is less than the incident radiation for the Stokes line, and the energy of the scattered radiation is more than the incident radiation for the anti-Stokes line. The energy increase or decrease from the excitation is related to the vibrational...

John Rennie

@EmilioPisanty In a quantum world all thing are possible, though you'd need to remain coherent for a while which might present some problems.

Emilio Pisanty

18:05

Stokes phenomenon

In complex analysis the Stokes phenomenon, discovered by G. G. Stokes (1847, 1858), is that the asymptotic behavior of functions can differ in different regions of the complex plane. These regions are bounded by Stokes line or anti-Stokes lines. == Stokes lines and anti-Stokes lines == Somewhat confusingly, mathematicians and physicists use the terms "Stokes line" and "anti-Stokes line" in opposite ways. The lines originally studied by Stokes are what some mathematicians call anti-Stokes lines and what physicists call Stokes lines. (These terms are also used in optics for the unrelated Stokes lines...

bolbteppa

and skip all the canonical stuff

Slereah

@bolbteppa you don't, but the alternative is worse

Emilio Pisanty

what did Stokes do to deserve that?

bolbteppa

What's the alternative

Slereah

The alternative is the weird ladder operators that depend on some test function

bolbteppa

18:06

You mean the functional stuff

Slereah

yeah

bolbteppa

Hmm

Slereah

Hm, can you do asymptotic stuff purely with path integrals

I think Weinberg might talk about it?

In the appendix

not sure

Captain Bohemian

does Weinberg write a book titled quantum field theory?

Slereah

Yes

bolbteppa

18:13

Weinberg wrote the bible, it's too hard

Slereah

no that was Jesus

bolbteppa

His approach is kind of amazing, 12 disciples, I mean cluster decomposition...

Captain Bohemian

I asked a question in math chat and somone told me the answer is in Weinberg's quantum field theory, but I don't have that book.

bolbteppa

I have it, what was the question

The hard cover of P&S is still one of the better covers ever, or Weinberg's cosmology

Semiclassical

@EmilioPisanty ugh yeah

Makes Googling a real pain

Slereah

18:16

the best cover is Spivak

Semiclassical

Especially since there’s inconsistency in the literature about Stokes vs anti-Stokes rays

Emilio Pisanty

@Semiclassical not if you're doing Raman stuff

bolbteppa

I have only seen old messy greying softcovers of Spivaks

Emilio Pisanty

> Somewhat confusingly, mathematicians and physicists use the terms "Stokes line" and "anti-Stokes line" in opposite ways. The lines originally studied by Stokes are what some mathematicians call anti-Stokes lines and what physicists call Stokes lines

thanks, Wikipedia, that clears it up completely.

Semiclassical

Lol

“Somewhat confusingly”

bolbteppa

18:19

I gave Stokes lines a go and ran away soon enough

Divergent series riemann surfaces scary scary

Emilio Pisanty

@bolbteppa yeah, I did that too some two-three years ago

bolbteppa

The Bender book in the references is great, man I want to know this stuff

Emilio Pisanty

it's easier the second time around

whoa

the Airy Bi function has complex zeros?

bejeesus

Captain Bohemian

@bolbteppa I don't know what the left derivative and right derivative in antibraket mean.

bolbteppa

What does that mean, can you give an example

Captain Bohemian

18:34

Doesn't Weinberg's quantum field theory define antibracket? It's in the Wikipedia article supermanifold en.wikipedia.org/wiki/Supermanifold

Slereah

18:50

@0celo7 best notation for the product $TU = T^{abc...} U_{abc...}$?

Maybe just $\cdot$ I guess

The proof of the integral by part is much simpler than I thought

Transcript for