The h Bar

bolbteppa

21:17

I guess that's why you only look at decay rates and cross sections

Finding out how to at least potentially consider n-particle scattering in the cross section took me so long and amounted to just a definition at the end of the day, conventions are such an unnecessary hindrance

The beauty $S_{10} = \int d^{10} x \mathrm{tr}(F_{MN} F^{MN} + \overline{\Psi} \Gamma^M D_M \Psi)$

How do you easily make $dx$ look nicer without mathrm all the time

Slereah

$\text{d}x$

bolbteppa

$\text{dx}$

Slereah

$\mathfrak d x$

bolbteppa

Your one is better

Too much typing to get it nice

0celo7

get the physics package and then \dd{x}

bolbteppa

21:27

Maybe that will work, but it gives an error on stack, $\dd{x}$, risky if I write everything using it then want to copy it to other places and it fails :(

Some good lazy shortcuts though apparently tex.stackexchange.com/a/275048/111183

This is actually an awesome package, is there a way to make $\pdv{x}$ $\pdv{f}{x}$ work on stack

Finally \tr gives trace, this is the best package ever

0celo7

@bolbteppa indeed it is

@BalarkaSen what a nightmare i.gyazo.com/e82adde0e92784b6b29c5b10e3d208a0.jpg

bolbteppa

Shortcuts really are a problem if you want to share the code though

\pdv*{f}{x} genius

To use '\dd x' or \dd{x}, that is the question

0celo7

21:43

@bolbteppa \dd{x} puts the right spacing.

bolbteppa

I was never able to get the right spacing, this is a nice fix, but stress of { }

It turns out the light-cone gauge is not evil and horrendous, it's actually absolutely vital

Slereah

Also I'd advise that once you find your ideal dx

Make a new command

So you can just type \dx

@bolbteppa it can be both

bolbteppa

I really hated the light-cone gauge, but now it's like the coolest thing ever, you need it to throw away a load of quadratic oscillators in the $\hat{L}_n \sim \hat{p} \cdot \alpha_n + \text{terms quadratic in oscillators}$ to make sure you can throw away ghosts!

Not explained well in Scherk but in GSW it is

light-cones > ghosts

Yeah \dd{x} is so good, can set up \dd{x} e^{-i\dv{f}{x}} so quick, now we use that insane delta method to solve it and then up is down, black is white!

0celo7

22:09

putting the measure before the integrand is degenerate

dmckee

@Slereah Someone did a study a few years ago of what topics ought to be in a introductory physics course for people going into health related fields.

Slereah

Relativity seems like a distant candidate

dmckee

They thought it weird that the topics we teach in those courses almost exactly match the ones taught in the first course for engineers and physics majors, and wanted to know what could be dropped.

Slereah

I mean, I guess time dilation might be a good solution to keep patients living longer

dmckee

They surveyed thousands of professionals in those fields. Very few individuals used more than a few topics. But every topics in the standard course was important to a few people.

Slereah

22:14

Is the QM part for radiation doctors

dmckee

Relativity is critcal in understanding beam mechanics for radiation physics, for instance.

So they ended the project with no useful recommendations, alas.

But when I'm running out of time I drop QM and relativity. I figure they are going to need a refresher when they start to specialize anyway.

0celo7

can't do QM without functional analysis or relativity without geometry

skullpatrol

you can't do anything without algebra

Slereah

what about gender studies

0celo7

the amount of algebra most people need is very minimal

I don't actually know what one does in algebra

Slereah

22:22

you learn the addition

0celo7

my main shelf has three sections

geometry, analysis, and physics

and the physics is all geometry and analysis

Slereah

Get some logic books

skullpatrol

^

bolbteppa

Ahah

The gruppenpest begs to differ

Someone once said to me only half-jokingly all of physics is representation theory

0celo7

the uninteresting parts, perhaps

GR is well defined and completely independent from algebra

amazing

Einstein knew de wae

bolbteppa

22:25

Said the diffeomorphism group representer

skullpatrol

lol

Slereah

@0celo7 tensor algebra

bolbteppa

Understanding tensors in terms of representations of GL(N) and Young diagrams and whatever else is involved is impossible

1

A: Relation b/w Dirac Algebra and Lorentz group

It's pretty annoying that P&S just give you $$S^{\mu \nu} = \frac{i}{4} [\gamma^{\mu},\gamma^{\nu}]$$ from thin air, here is a way to derive it similar to Bjorken-Drell's derivation (who start from the Dirac equation) but from the Clifford algebra directly, assuming that products of the gamma ma...

0celo7

@Slereah that's not real algebra

Slereah

One of my master thesis was Young diagram stuff

The $SU(2)$ part was alright

0celo7

22:28

real algebra is homological galoid functors on derivative Grothendieck sheaves

Slereah

Then I had to do $SU(3)$

And all went to hell

bolbteppa

I find it impossible

Young Diagrams arise in multiparticle QM very naturally and I still can't make sense of this stuff

Slereah

yeah they pop up a lot for like

Baryons and mesons

Since you can do decomposition of products of $SU(N)$

And the composite particles are $\approx$ the irreps

bolbteppa

I've managed to avoid it all and it's getting more annoying avoiding it, really want to get this stuff down

Slereah

It's like

If you pick some sigma model of two particles

For quarks

Then it's some $SU(2)$ vector

The product of two such vectors will be $\frac 12 \otimes \frac 12 = 1 \oplus 0$

The vector part is composed of the three pions

And the scalar part some other meson

bolbteppa

22:33

I'm happy breaking up a 3 x 3 matrix into it's trace, a symmetric matrix, and an anti-symmetric matrix, which is a $3 \times 3 = 1 + 5 + 3$ or whatever

Slereah

yeah that's the real thing behind it

It's like $q_\mu q_\nu = q_{[\mu}q_{\nu]} + q_{\{\mu}q_{\nu\}}$

It gets much more annoying for $SU(3)$ though

0celo7

just get Zee's book

I bet it's nonsense but gives formulas for this shit

Slereah

For the SU(3) part i had to read the worst book in the world

The math book written entirely in Penrose notation

Clebsch–Gordan coefficients for SU(3)

In mathematical physics, Clebsch–Gordan coefficients are the expansion coefficients of total angular momentum eigenstates in an uncoupled tensor product basis. Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations, where the type and the multiplicities of these irreducible representations are known abstractly. The name derives from the German mathematicians Alfred Clebsch (1833–1872) and Paul Gordan (1837–1912), who encountered an equivalent problem in invariant theory. Generalization to SU(3) of...

And now, 6 years later, there's just a wikipedia article about it

0celo7

hmm

is there automatically a maximum principle when the first Dirichlet eigenvalue is positive?

Jake Rose

Anyone free for a quick wave and sho conceptual question?

Slereah

22:49

$$|y, \gamma, {i^2}, {i^z}, c^1, c^2\rangle =\sum_{y_1, y_2}\sum_{{i^2}_1, {i^2}_2}\sum_{{i^z}_1, {i^z}_2}\langle y_1, y_2, {i^2}_1, {i^2}_2, {i^z}_1, {i^z}_2|y, \gamma, {i^2}, {i^z}, c^1, c^2\rangle |y_1, y_2, {i^2}_1, {i^2}_2, {i^z}_1, {i^z}_2\rangle$$

What is this madness

I mean it's just the old completeness thing

still

quite awful

bolbteppa

Hook length

God

0celo7

@Slereah nice

skullpatrol

@Slereah how many pages was your thesis?

bolbteppa

amazon.com/…

That book is read by physicists, I mean...

Slereah

40 maybe?

0celo7

22:56

how goofy

bolbteppa

There are no equations or symbols on the dog...

0celo7

wonder what the dog is supposed to represent

skullpatrol

dogma?

0celo7

I am on the upshot of my understanding sine curve

skullpatrol

Is your learning curve also sinusoidal?

Slereah

23:03

The dog represents simplicial complexes

0celo7

@skullpatrol at this point in my career it seems like a vertical cliff wall

bolbteppa

Mine

skullpatrol

lol

0celo7

The situation in geometric PDE is really bad because the details get out of control very quickly

skullpatrol

Whatever happened to the Yugoslavian PDE guy?

0celo7

23:08

he's probably busy

skullpatrol

yeah, he travels a lot

0celo7

and like half of the field is in journals and lecture notes

to the credit of algebra and topology, they seem to have a lot of foundational textbooks for the higher stuff

skullpatrol

lower stuff too

0celo7

we've got Gilbarg and Trudinger and you're fucked if you need anything that's not in there

for geometric PDE there's basically the books on my profile

and most of those are lacking severely

there's also Federer which is cancer

you can read Simon but it doesn't have all the details and then you read Federer and it's still cancer

and depending on how much faith you have in things, you need to learn basically all of Reed and Simon too

well, that's an exaggeration

but it certainly doesn't hurt to know spectral PDE

semigroups and representations of differential operators

bolbteppa

23:42

I think we all need to know R&S Vol. 1 at some point, just looking at it now and again is useful slowly over time

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