The h Bar

6:35 AM

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

7:02 AM

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

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

7:18 AM

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

@ManasDogra yes, precisely

7:29 AM

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 $\phi(w, \bar w)$.

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…

9:13 AM

@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

9:32 AM

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 $z = \mathrm{e}^t\mathrm{e}^{\mathrm{i}x}$

9:43 AM

@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

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

@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 AM

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

12:05 PM

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…

1:37 PM

vixra.org/abs/2205.0133

1:54 PM

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

and unrelated

I guess it's a common name

2:52 PM

@Slereah it's a very common German name

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

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…

6:13 PM

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)

what do you mean by "polarized particle"?

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

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

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

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

6:17 PM

@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?

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

@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?

@MauroGiliberti invariant under what?

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

@ACuriousMind That makes sense

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

6:33 PM

I'm not sure what you mean

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

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)