@EmilioPisanty do you think mathcha.io/editor would be a good candidate for a community ad? Also, would one need to come out with an original figure for a proposal? I would just go ahead and use the website's logo for it but I'm not sure that's proper

You know I wonder, if someone did a survey of usage, what would "well-behaved" mean in math in general

I assume most of the time it means "continuous"

@Slereah "having exactly the properties needed to make what I'm saying true" :P

@ACuriousMind Well yes, but what would that be in general!

impossible to say!

that's why people say "well-behaved" instead of something more specific :P

I mean it would be hard, but it should be doable

Look at a paper, find the usage of "well-behaved", work out the math to find out what class of objects for which this is true

tabulate the results

I just suspect while it will often include "continuous", it will almost never mean just that, since "continuous" is exactly as quick to say as "well-behaved"

probably

and what specific things are required will depend a lot on what subfield you're looking at

Continuous, derivable, measurable, integrable, etc etc

Also importantly

Do people use "well-behaved" and "nice" differently

can a function be well-behaved but not nice

Majorana spinor for dummies

Is there a specific reason why the spinor metric is $\sigma_2$?

People just show the calculations, but is there any deeper reasons for it

Plus $\sigma_2$ is a specific choice of basis for $SU(2)$, so it feels a bit weird that a random basis element of the algebra would be the metric

The spinor metric is the Levi-Civita tensor (which can be written as $\pm i \sigma_2$ depending on how you choose things), which is invariant under $\mathrm{SL}(2,\mathbb{C})$ (the way the Minkowski metric is invariant under $\mathrm{SO}(1,3)$)

Is there no meaning in the fact that it's one of the pauli matrices also?

and a specific one at that?

@Slereah no, the $\sigma_i$ thing is specific to a choice of basis

Hm

$\sigma_2$ is related to the spinor metric, $\sigma_3$ is related to the helicity projection

I wonder if $\sigma_1$ has a special property

@Slereah $\sigma_3$ is only related to the helicity if you've rotated into a frame where the momentum is along the 3rd direction

Permanent?

@ACuriousMind I mean it's something at least

Nice and diagonal

if you rotate into a frame where momentum is along the 1st direction, then $\sigma_1$ takes its place :P

I don't think I've ever seen $\sigma_1$ used for anything outside of being a sigma matrix

@ACuriousMind I mean sure, but then you have an ugly mixed spinor!

I assume they write it as $i \sigma_2$ because it's a nice quick way to write Levi-Civita as a matrix

You know what's shorter

$\varepsilon$

Yeah but that's an infinitesimal parameter!

Especially in susy it's usual notation as the infinitesimal parameter so

$\sigma$ is the scattering cross section!