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Daniel Underwood

00:56

"simple steak" could be a pretty good description of us to the bear!

6 hours later…

Manas Dogra

06:35

How do we get the $z^{-h}$ and $\bar{z}^{-\bar{h}}$ factors in the Laurent expansion?

Nihar Karve

07:02

@ManasDogra from the conformal transformation from the cylinder to the plane

Manas Dogra

Can you say exactly how so?
Must be something really very simple I think...

Manas Dogra

07:18

Are we actually expanding $\phi(w,\bar{w})$ where $z=e^w$? Then I would get those factors right from the definition of a conformal field

Nihar Karve

@ManasDogra yes, precisely

Nihar Karve

07:29

to be clear, under $w\to f(w)=e^w=z$

$$\phi(w, \bar w)\to (\partial_w f)^h(\partial_{\bar w}\bar f)^{\bar h}\phi(f(w), \bar f(\bar w))
\\\partial_wf=z
\\\phi(f(w), \bar f(\bar w)) = \phi(z, \bar z)=z^{-h}\bar z^{-\bar h}\phi(w, \bar w)
$$
and then expand $\phi(w, \bar w)$.

Manas Dogra

Yes, that's what I was thinking..Thank you.
Another question-I was thinking $e^{x_0}$ to be radii of the circles on the complex plane which we get after mapping, where $w=x_0+ix_1$, but it turns out $x_0$ is imaginary, then how can we interpret like above or can't we?

I have seen places telling that as the time increases the radius of the circle increases...(since The radius is $e^{x_0}$)
But with $x_0$ imaginary, the radius is 1, how can it increase as time increases?

2 hours later…

Nihar Karve

09:13

@ManasDogra I never keep track of this properly, but I think the idea is to define a Euclidean coordinate $x^2 = ix^0$ first, then actually take the mapping of the Euclidean theory via $e^{x^2+ix^1}$

since translations of the Euclidean time coordinate should generate dilatations of the complex plane, as you say

ACuriousMind

09:32

when you describe the cylinder in normal plane coordinates $(t,x)$ with $x \sim x + 2\pi$ with $2\pi$ the circumference of the cylinder, the map to the complex plane with coordinate $z$ is $z = \mathrm{e}^t\mathrm{e}^{\mathrm{i}x}$

Manas Dogra

09:43

@ACuriousMind Yes that's what I thought initially but then while defining hermitian conjugate of a primary field, it was said that t goes to -t

ACuriousMind

@ManasDogra ah, yes, that's what Nihar said - the theory on the complex plane is Euclidean, so there's a Wick rotation $x^0 = \mathrm{i}t$ hidden here

see physics.stackexchange.com/q/87789/50583

2 hours later…

Emilio Pisanty

11:29

A: Is it okay to start a sentence with a Greek letter (variable)?

In more scientific/mathematical writings it may be more acceptable to start a sentence with a symbol, if only because of their higher profusion in texts and because the need for such constructions is frequent enough that rephrasing all of them may make a text a lot clunkier. In particular, I not...

man, look at me-from-nine-years-ago go!

I'm often surprised when answers by that kid turn up and they're rather better researched and thought-out than I would expect from early posts

Slereah

12:05

The worst notation I have one seen is someone putting a footnote marker next to a variable

$n^2$ where the 2 referred to a footnote

2 hours later…

Slereah

13:37

vixra.org/abs/2205.0133

Slereah

13:54

Klein-Gordon Klein and Klein geometry Klein are two different people it seems

and unrelated

I guess it's a common name

ACuriousMind

14:52

@Slereah it's a very common German name

Slereah

Probably similar to Petit in French

You know who is named Petit?

Jean-Pierre Petit

Jean-Pierre Petit is a French engineer who authored the comic book series The Adventures of Archibald Higgins. == Early life == Jean-Pierre Petit obtained his engineer's degree in 1961 at the Institut supérieur de l'aéronautique et de l'espace (Supaéro). Petit defended his doctoral thesis, Applications de la théorie cinétique des gaz à la physique des plasmas et à la dynamique des galaxies, at the University of Provence in 1972. == Art == In topology, Petit worked with Bernard Morin on the torus and sphere eversion. In the 1980s, he taught sculpture at the art school of Aix-en-Provence, where...

Crazy man Jean-Pierre Petit

ACuriousMind

it means "small" in modern German, but it had more and more positive meanings in older German (it's cognate with English clean)

3 hours later…

Mauro Giliberti

18:13

Hello all! Where can I read something about polarized scattering, from a theoretical point of view?

I can't seem to find a comprehensive source that explains how to treat, generally, a scattering between polarized particles (I'm interested in photons but now I'm just curious about the whole idea)

ACuriousMind

what do you mean by "polarized particle"?

Mauro Giliberti

for example, a photon with a definite polarization (definitely right-handed, for example)

ACuriousMind

Just a particle that has polarization? Polarization is not really different from the spin of massive particles, if you know how to e.g. scatter a spin 1/2 fermion you should also know how to scatter a photon

Mauro Giliberti

But I don't know hot to scatter a fermion either lol

I mean I know how to, but never used the fact that it's in a specific polarization

ACuriousMind

there's often a sum over ingoing/outgoing polarizations/spins in scattering amplitudes because we don't really have definite spins/polarizations in real-world colliders

the way to scatter something with a definite spin/polarization is just to omit that sum

Mauro Giliberti

18:17

@ACuriousMind clever

so it is like if I have many diagrams for the same process, I sum over all the possible diagrams?

and for polarization, I sum over every possible polarization?

ACuriousMind

spin/polarization doesn't make different diagrams

a non-scalar particle has indices attached to its propagator that get contracted at vertices and remain "open" at external legs

usually we sum over these "open" indices to indicate we are scaterring stuff whose spin/polarization is uniformly distributed

but if you have a specific spin/polarization, then you just pick the index corresponding to that instead of summing

this is completely disjoint from the perturbative sum over diagrams

Mauro Giliberti

@ACuriousMind that's what I mean

@ACuriousMind yes, I know, I meant that in the same way as, with different diagrams, we sum over them, we also sum over polarizations, but I'm aware that it's a different thing because I can, in principle, know what polarization I have but knowing "which diagram I have" makes no sense

If I have a specific polarization and therefore I get to "pick the index", what is the thing that I have? is it invariant? is the sum of all the "specific polarization" invariant? if I know it, can I change polarization and know something about the new polarization?

ACuriousMind

@MauroGiliberti invariant under what?

of course a specific spin/polarization will not be Lorentz invariant - it picks out a direction

Mauro Giliberti

@ACuriousMind That makes sense

But can I build a Lorentz invariant knowing the many specific polarizations?

ACuriousMind

18:33

I'm not sure what you mean

Mauro Giliberti

physics.stackexchange.com/questions/715078/… This is the question that started my doubts

ACuriousMind

change of polarization basis has nothing to do with Lorentz invariance

but why would the sum of matrix elements be invariant under basis change?

that's not true even for ordinary matrices

what's true is that the trace is invariant, i.e. $M_{++} + M_{--} = M_{xx} + M_{yy}$ is what you should expect (and that's why you seem to "derive" $M_{xy} = M_{yx} = 0$ there)

Mauro Giliberti

@ACuriousMind that's enlightening actually

it's an actual matrix basis change

1 hour later…

Emilio Pisanty

20:10

@Slereah I was proofreading a friend's thesis and it had things like $A_{ec}$ distinct from $A_{e'c'}$. And it was all fine until those started appearing immediately before commas in the sentence.

if you had them side-by-side you could tell them apart, but in isolation it was damned hard

@Slereah I'm sold by the cover