The h Bar

John Rennie

4:05 PM

Should group names like SU(2) be mathjaxed? If so $SU(2)$ or $\mathrm{SU}(2)$ ?

AccidentalFourierTransform

IMO the latter looks best

Slereah

Hm

ACuriousMind

@JohnRennie I am of the opinion that they should be, in \mathrm

Slereah

I don't think the complete feather can be embedded in a manifold unless it's like $\Bbb R^\omega$, even if we identify the adjacent points

ACuriousMind

I find it jarring to have SU(2) in text just talking about the group and then $\mathrm{SU}(2)$ (or $SU(2)$, if you don't care about upright names) when you want to write down e.g. a map $f:\mathrm{SU}(2)\to X$.

Slereah

4:08 PM

the basic feather would be embedded in $\Bbb R^2$ and look like the upper half space

Double feather in $\Bbb R^3$

etc etc

John Rennie

@ACuriousMind hmm, Qmechanic disagrees

AccidentalFourierTransform

$\mathrm{Qmechanic}$

ACuriousMind

@JohnRennie Many do. I'm on the extreme end of the scale when it comes to reserving not-mathrm'd letters only for variables.

Slereah

mathrm for groups I'd say, yes

and mathfrak for the algebra :p

I'm not sure what mathscr would be for

0celouvskyopoulo7

He disagrees?

With the upright thing?

Slereah

4:12 PM

$\mathscr{SU}(2)$

gross

0celouvskyopoulo7

It's universally accepted that it should be upright

Just as -+++ is universally accepted

AccidentalFourierTransform

:: remains silent ::

Slereah

The only good way to do GR is with octonions, of course

I wonder what the metric looks like in that GR with octonion paper

let's see

uhoh

3

Q: Why doesn't thermal radio emission from a DSN "hot dish" completely swamp the benefits of a cold LNA?

The 70 meter DSN dishes are often used to receive the weakest signals, and so their receiver LNAs have cryogenic front-ends in an assembly that also contains a LHe refrigerator and vacuum system. If I understand correctly these are located in the "feed cones" pointed at the Cassegrain secondary r...

needs some physics attention?

Slereah

"ON FACTORIZATION OF EINSTEIN'S FORMALISM INTO A PAIR OF QUATERNION FIELD EQUATIONS"

oh it was quaternions

Naveen Balaji

4:18 PM

Hey guys! Been stuck with this for a long time now, please do help

3

Q: On reducing complex ODE's to Bessel's form

I am trying to reduce the following ODE to Bessel's ODE form and solve it: $$x^{2}y''(x)+x(4x^{3}-3)y'(x)+(4x^{8}-5x^{2}+3)y(x)=0\tag{1} \, .$$ I tried to solve it via the standard method, i.e., by comparing it with a generalised ODE form and finding the solution from then on. The general form (...

differential-equations bessel-functions frobenius-method

Slereah

The quaternion metric is expressed as $$g^{\mu \nu} (x) = - \frac 14 \mathrm{Tr} (q^\mu \tilde q^\nu + q^\nu \tilde q^\mu)$$

where $q$ is a quaternion

it's the best metric

Though to be fair, I think this is basically thinly disguised GR with spinors

Since quaternions are $\approx \mathrm{SU}(2)$

Physics Guy

Quaternions are good.

Slereah

Basically the quaternion $q$ is just $\sigma^\mu e_\mu$

Where $\sigma$ is the Dirac matrix/imaginary units

So it's basically $q^\mu = e^\mu_t + e^\mu_x i + e^\mu_y j + e^\mu_z k$

Physics Guy

@Slereah Who are you talking to?

Slereah

The room

Feel free to respond at any time

Physics Guy

4:29 PM

Okay.

Hi, everybody.

Hello

Hello

Any help on this ? SAXS is preferred for nano material characterization then that of XRD

Slereah

nanomaterials are very small

I would use my tiniest hammer

BAYMAX

4:34 PM

:)

any reference will help too! I searched but got none ><

Slereah

Whatever happened to quaternions

They were all the rage in physics and then everyone forgot about them

though we still use them a lot, we just call them Dirac matrices now

Physics Guy

Yeah, I was just about to say that.

Quaternions play a huge role in the physicists everyday life.

Slereah

it just has become unfashionable to call them quaternions

How does one represent spinors with quaternions, I wonder

AccidentalFourierTransform

using the spinor-quaternion lemma

Physics Guy

@AccidentalFourierTransform definition?

AccidentalFourierTransform

4:42 PM

something about vector spaces

0celouvskyopoulo7

@ACuriousMind if you were to teach an intro QM class would you try to insert any Rigor?

Haha my phone autocorrected to a capital R

Slereah

considering the rigor needed for QM that might make for a long class

also you'd be mostly loss when reading QM books

Considering that for most physics books, the adjoint means "just replace $i$ by $-i$"

0celouvskyopoulo7

You have to do an incredible amount of work to show there's an eigenbasis

(In certain cases)

Slereah

also the eigenbasis isn't even an eigenbasis for most physics applications

is $\hat x$ even an observable, since you can't really have a particle in an $\vert x \rangle$ state

AccidentalFourierTransform

sure you can

Slereah

4:51 PM

Can you

AccidentalFourierTransform

for example, let $\hat x=\sigma_z$ and $|x\rangle=|+\rangle$

Slereah

What

AccidentalFourierTransform

there you go

0celouvskyopoulo7

...

AccidentalFourierTransform

I just fixed QM

you thank me later

Slereah

4:52 PM

What if I let $\mathrm{AccidentalFourierTransform} = \mathrm{A smelly man}$

0celouvskyopoulo7

Use \text ffs

Slereah

You're not my mom

AccidentalFourierTransform

ಠ╭╮ಠ

John Rennie

@BAYMAX the X-ray scattering angle is inversely proportional to the size of the object doing the scattering. Nano structures tend to be around a few nanometres in size, and the scattering angles for this size range are smaller than the angles easily measurable in XRD.

That's why we tend to use small angle scattering for nano sized structures.

Slereah

I should make a latex shortcut for ^{-1}