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12:00 AM
hmm , I think I need something clearer lol
I am cursed. . I can't understand it lol
 
@Danu I know
I had this notion that it might also refer to penrose notation for some reason tho
 
hi guys can i delete an old post of mine that I feel is useless for this website (physics.stackexchange.com/questions/172360/…) , it drew almost no attention, etc
it's a homework type of post
 
@no_choice99 If you see the "delete" text at the lower left of the post you can delete it.
I believe the system only prevents owners from deleting material that has upvoted answers or is locked by a moderator.
 
ok thank you very much
 
12:22 AM
ok finally figured it out . . . physics.ohio-state.edu/~mathur/italy1.pdf
was not that hard either, just a lot of substitution, then some regular plots accompanied by new vocabulary
exciting stuff
Just got panda express . . . . yeeehaaaa!!
So what I have learned so far from trying to do path integrals- - - I never really learned calculus well enough
----- QFT is a big integration orgy
 
QFT has a shitload of integrals
especially once you start doing loops
 
It's amazing people actually sit down and compute these things. I used to think at least some computer thing could understand and help in analytically computing these things but neh, gotta do it by hand lol
I am going to go for a run and then come back , and try to see if today would be the day I understand some of the gr things that have been eluding me for years. Hopefully I can find a gr book that is written in the spirit of anthony zee. Zee reduced the path qft to a regular integral, and introduced feynman diagrams at that point already, then upped the anti gradually . . . . . till the end. It was quite an enjoyable excursion.
 
1:17 AM
@0celo7: Something to chuckle for you: Are Bajorans of human origin?
 
1:45 AM
@kevinTahN. No one learns calculus well enough until they have to really apply it. Except Feynman, of course.
 
2:00 AM
Hey does anybody have a copy of library.seg.org/doi/abs/10.1190/1.1441417 ?
My school's library apparently doesn't have it...
 
This hat is just great
 
2:45 AM
Feynman creates calculus for his own understanding @dmckee
According to his quote, what I cannot create, I do not understand
 
yeah, but he also boasted a lot
 
That's his personality.
 
@skullpetrol He could've created a well-defined path integral then :P
 
3:34 AM
Susskind said Feynman always looked for the simplest way to approach problems.
Feynman's scientific style was always to look for the simplest, most elementary solution to a problem that was possible. If it wasn't possible, you had to use something fancier. But no doubt part of this was his great joy and pleasure in showing people that he could think more simply than they could. But he also deeply believed, he truly believed, that if you couldn't explain something simply you didn't understand it.
His creations that he did understand must have been made as simple as possible.
 
I would argue that the fields have grown more complex, since his time, and that today a simple explanation is not feasible.
 
3:55 AM
For some things, yes.
But the danger of not being able to see the forest for the trees will always exist.
 
4:45 AM
@dmckee Feynman is the man. I recently read "Quantum man" by Krauss. There are all sorts of achievements attributed to him that I was not even aware of. Also yes, I am only beginning to appreciate how far calculus can go. I need to work hard to be able to begin applying it. The good all days of just calculating areas, volumes, velocities etc are long gone. I have to be an adult now lol
Feynman is the man.
 
 
2 hours later…
6:51 AM
@kevinTahN. functional integration, I highly doubt, but there is SymPy for doing some symbolic calculations in Python.
(and incidentally half the point of Wolfram Alpha is to show step-by-step solutions for things)
 
7:13 AM
well automatic integration exists, but its probably harder compared to get a mathematica document to integrate for you...
 
 
2 hours later…
user54412
9:03 AM
So we have tags , , , and . Thoughts on redirecting all of these to ?
 
well that statics are different...
Fuck, I have a large project due in 10 hours and I can't do the derivation.
Help me o'atheist god
 
 
2 hours later…
11:06 AM
I'm alive.
@Mikhail Dawkins can't help you physics
@kevinTahN. What else do you do with calculus that is not a fancy version of the things you just listed
@ACuriousMind I already know the answer Mr. Ayy Lmao
Also fancy hat...
 
11:20 AM
@Slereah dear god
 
What do you guys think of my answer for this: physics.stackexchange.com/q/223788/6049
 
@Slereah we should write a GR book in only penrose notation
@Slereah just scan in our drawings
 
11:49 AM
There is a group theory book all in penrose notation
 
I know
@Slereah apparently $\Lambda^kT^*$ is a functor on $\mathsf{Diff}$
@Slereah hmm apparently the dimension of a manifold can be nonconstant across the manifold
 
wot
What manifold has non-constant dimensions
 
a non-pure manifold
 
Huy
wat
stop trol statements
 
fu
apparently topology only says that $n$ is locally constant
 
11:59 AM
what's an example tho
also what's the transition function between atlases gonna be
 
no clue
 
Huy
just lies
empty statements
so bad
 
example: $S^1\sqcup\mathbb{R}^2$?
 
Hm, I guess
So only disconnected manifolds, tho, mb
 
we could ask the math chat
 
Huy
12:03 PM
who on earth would want to define manifolds to allow such things
 
well according to this book the definition of manifold does not forbid it
 
Huy
well yeah, if you define them differently than usually
usually you define an $n$-manifold as something that is Hausdorff, 2nd countably and locally homeomorphic to an open set in $R^n$
never seen anyone define a "manifold" as some object such that for each neighbourhood there exists a natural number $n$ such that ...
 
Huy
he fixes $n$ so he's contradicting himself
what book is that
 
"Natural Operations in Differential Geometry"
 
Huy
12:10 PM
what are you reading it for
 
GR
wtf is a germ, anyway
 
Huy
equivalence class
 
I can read wiki too
what does that mean
 
Huy
ok then read wiki
 
no
 
Huy
12:16 PM
then prove that the different definitions of tangent vectors coincide
 
I've done that before
it's quite boring
 
Huy
ok
then why don't you know what germs are
 
I did
 
This is a germ
 
12:17 PM
I just forgot
 
Huy
can you prove that the usual basis vectors for the tangent space are linearly independent with the germ definition
 
The proof of that is in Wald. Or Straumann.
 
Huy
so Wald and Straumann can
 
yah
 
Straumann, Straumann
Can do whatever a Strau can
 
Huy
12:20 PM
@0celo7 is that just a DG book or something else?
 
@Huy GR
 
Huy
ah ok
are there any somewhat common applications of $RP^n$ in physics?
 
string theory
 
Huy
your favourite field right
 
no
 
Huy
12:22 PM
:(
 
I would be more interested in it if 1) there were good books on it 2) SUSY didn't suck
3) physicists could explain group theory
 
Huy
what's SUSY
there's an intro course on it next semester at my uni
wondering if I should attend it to see what it's about
 
@Huy is that what you wanted
 
SUSY is supersymmetry
It is the maximal extension of the Poincarré group or some shit I forget
With group elements to switch between representations
 
Huy
that's $\{0\}$
@0celo7 I know some group theory
 
12:25 PM
can you calculate tensor products in $E_8\times E_8$
 
Huy
Basics of string theory, including
(1) The quantisation of the bosonic string (covariant and light-cone quantisation);
(2) World-sheet description of strings in terms of conformal field theory;
(3) Compactification and T-duality, low-energy description of string theory;
(4) D-branes.
ELI5
 
No this is it
 
Huy
maybe if I cared about it
 
@Huy that's the easy shit
 
Huy
well yeah it's an intro course
 
12:26 PM
not superstring theory
 
Huy
it says intro to string theory
not superstring theory
so ELI5
 
ok well that's fine
 
You can also just read non-string SUSY
 
did he get banned
 
Huy
no
 
12:28 PM
Did I?
 
@Huy so is that what you wanted me to prove??
 
Huy
no but nvm
ELI5 what I'd learn in that course
I wanna see if it's at all interesting for me if I don't do anything more than that intro
 
do you want some lecture notes that cover that stuff?
 
Huy
no I want an ELI5 from you tl;dr
 
you'll see that the string contains the graviton
 
Huy
12:30 PM
if you ask me "what do I learn in functional analysis" I would try to summarize some of it and not give you a book
 
then the prof will go ape shit and say string theory needs more funding
 
Huy
what's graviton
 
quantum of the gravitational field
 
Huy
we have enough funding
over here profs don't need to beg for more funding
 
Gravitons are closed strings
Well one mode of a closed string, IIRC
 
12:31 PM
basically you will show that the closed string has several modes
 
From what I vaguely recall closed strings pull double duty as graviton and dilaton
 
graviton, Kalb-Ramond and dilaton
 
What is Kalb Ramond
 
two-form gauge field
 
gross
 
Huy
12:32 PM
is it true that nothing in String theory is yet verifyable because we can't do such measurements yet
 
the dilaton gives you the expansion parameter in the string perturbation series
also some shit with the Euler number of the worldsheet
it's not very interesting tbh
@Huy well it reproduces everything we know of, sorta
but I'm not sure what the new predictions are...and we certainly can't measure them
 
Huy
what's the 7 or 8 dimension fuzz about
 
it's 26, 11 or 10
 
Huy
ah ok
for what? for the world we live in?
 
26 in baby string theory
11 in super string theory
10 in M theory, which is not a string theory
but somehow string theorists study it...not sure what that's about
I quit trying to string theory when there were stupid things like 246 dimensional reps of $E_8\times E_8$ floating around
 
12:35 PM
heheh
 
and then they threw in some dynkin diagrams for fun
 
Huy
for what? for the world we live in?
I know some dynkin diagrams
 
for $E_8\times E_8$
 
Huy
and what does E_8 \times E_8 model
 
or $\mathrm{SO}(32)\times\mathrm{SO}(32)$
 
12:36 PM
much simpler
 
at least I know what the fuck $\mathrm{SO}(32)$ is
 
What is it
 
32-dimensional special orthogonal matrices
 
Is it 5 bits of rotation
Well yes but why 32
 
because Witten
 
12:37 PM
what is it rotating
Flavors?
 
meat
 
Huy
ok so not interesting
 
waits for @ACuriousMind to see the horror
 
More importantly
Do they have a diagram for SO(32)
Maybe some Young tableaux
 
no
 
12:39 PM
Or maybe
Penrose notation for SO(32)
 
Huy
one of my profs hated penrose
 
he might have had a good reason
 
Huy
he said that some scientists are really good at research and some are really good at selling themselves well, and that penrose belonged to the second group
 
String theory ^
 
Help
 
Huy
12:43 PM
I need somebody
 
Isn't $B_{\mu\nu}$ the torsion field
I seem to recall something like that
 
I think it is...
I don't really care anymore.
@Huy for?
did you ever complete that calculation?
 
Huy
maybe after the pedagogy "exam"
I am "studying" for it atm
 
so why do you need somebody
 
Huy
cuz Paul said so
 
12:51 PM
Paul?
 
Huy
..
 
dunno who Paul is
@Huy ??
 
Huy
@0celo7 !!
this is such a waste of time
 
1:41 PM
@ChrisWhite I think the statics tags are fine, the -fields can go
 
1:53 PM
@Huy what
 
Huy
@0celo7: pedagogy shit
20mins till exam
 
@ACuriousMind you should give @Huy the tl;dr on string theory
I'm too confused to do it
Haven't slept in a while
 
I don't think there is a tl;dr on string theory
 
@ACuriousMind he wanted one
chat session!
 
@0celo7 Uh...it starts in 2 hours
 
2:05 PM
@ACuriousMind Being in your time zone is crazy
 
2:17 PM
@ACuriousMind how does one live 6 hours ahead of civilization
 
My barbarian mind does not understand this question.
 
@ACuriousMind Ooga booga frooga doo?
 
2:29 PM
SUSY, where are you?!
Don't leave us!
For those who missed it: The CMS announcement just revealed that there are no SUSY signals in their current data.
 
@0celo7 define civilization
 
@yuggib people who live in [GMT-5].
 
@Danu That'll make a lot of people quite sad
 
@0537 Then I prefer to live in uncivilized countries where you can find something e.g. like this:
 
I'm too dumb to do the ODE $f''-\frac 2gf'g'=0$, $f$ and $g$ being both variables in $x$. I tried to divide by $f'$, getting $f''/f'=2 g'/g$. How to continue? Both sides could be any function of $x$, can't they?
 
2:37 PM
@Bass Hint: Logarithms.
 
2:53 PM
ba dum tss! thanks!
 
3:33 PM
it's always logarithms
 
Anyone know what the numbers under your little avatar in chat mean?
 
For example, @yuggib has 4507 underneath.
 
I think it's supposed to be total network-wide reputation
oddly enough I'm not seeing those numbers now
 
Chat session?
 
3:35 PM
Half an hour-ish
 
I've asked this before, but...
Anyone have any idea how to think about expressions like $\int dx \, \delta (f(x,y))$?
 
as in the Dirac delta function?
 
@DavidZ Yes.
 
Hm. Well, if you want mathematical rigor, I have no idea, but in practice I consider it to be an integral over the subspace on which $f(x,y) = 0$
oh wait, that'd be if it's $\int \mathrm{d}x\, \mathrm{d}y\, \delta(f(x,y))$
hmm...
 
@yuggib U.S. of A.
 
3:40 PM
@DavidZ Yes, indeed.
 
@DanielSank For "nice" $f$, you have $\delta(f(x)) = \sum_i \frac{\delta(x-x_i)}{\lvert f'(x_i)}$ for the real roots of $f$.
 
@ACuriousMind Indeed, but what happens when I want to integrate over one variable?
 
Treat $y$ as a constant, I suppose
 
@DavidZ Right, if we were integrating over all space we could e.g. parametrize the manifold on which the function is zero and then just do the integral.
@DavidZ I'm having trouble understanding what that means.
 
>manifold
 
3:42 PM
Treat it like 5 :-P
I mean, can you elaborate?
 
it could be some plane curve which has self-intersections, no?
 
So, you get $\int \delta(f(x,y))\mathrm{d}x = \sum_i \int \frac{\delta(x-x_i)}{\lvert f'(x_i,y)\rvert}\mathrm{d}x = \sum_i \frac{1}{\lvert f'(x_i,y)\rvert}$ since $\int \delta(x)\mathrm{d}x = 1$.
Hmmm
 
@DavidZ Thinking.
 
I see your problem now, if I write another $y$-integral the results are completely different depending on how one expands the $\delta$.
 
@ACuriousMind huh?
 
3:46 PM
@ACuriousMind This seems wrong.
 
what is $f'(x_i,y)$ even
 
Ah, the $x_i$ don't make sense!
 
@0celo7 It's probably $\partial f / \partial x$.
 
@ACuriousMind exactly
 
$f(x,y)$ doesn't have roots "in one variable"
 
3:47 PM
^^
that's a middle school mistake, mister
 
So...I'd guess $\delta(f(x,y)) = \sum_i \frac{\delta(x-x_i)\delta(y-y_i)}{\lvert \nabla f(x_i,y_i) \rvert}$ for $(x_i,y_i)$ the roots of $f$.
 
^^
 
But it is probably wrong, the denominator especially could be different
 
@ACuriousMind Interesting.
 
@ACuriousMind how does one prove it in 1 dimension again?
 
3:49 PM
@ACuriousMind Actually I bet that's right and can be proved in the same way as for one variable.
 
I'll try to derive it.
 
linear expansion and change of variables?
 
@0celo7 It's easy:
$f(x) \approx f(0) + x \, (df/dx)(0) + \cdots$
 
so...what I just said
 
@0celo7 Yes, jeezus I was typing.
 
3:50 PM
@DanielSank Ah, yes, you are right, the Taylor expansion just gives the gradient.
 
@ACuriousMind yeah
 
Write the delta distribution as the limit of a mollifier
substitute in the mollifier argument the function $f(x,y)$
and compute the integral in $x$
then take the limit and you should get the distribution corresponding to $\int dx \delta(f(x,y))$
of course it should only be true for regular enough $f$s
 
Assuming $x$ and $y$ are independent, it should work out that $$\int\mathrm{d}x\,\delta(f(x,y)) = \sum_{i: f(x_i,y)=0} \frac{\delta(x - x_i)}{\partial_x[f](x_i, y)}$$
I think
 
@DavidZ the condition $f(x_i,y)=0$ doesn't really make sense unless you expect that $f$ is zero on an entire line
 
@yuggib Yeah that works too, but I was hoping to see it another way.
 
3:54 PM
@0celo7 : Hm.
 
@0celo7 Wrong way around, 11 in M theory, 10 for superstring, I think.
 
@ACuriousMind Thanks for the push. The important thing, in some sense, is that the first order terms in a multi-variable Taylor expansion only involve one variable at a time.
 
@ACuriousMind I don't see what you mean... $f(x_i, y) = 0$ seems like a perfectly sensible equation, and given $y$ you can find values of $x_i$ for which it holds
 
@DavidZ Oh you mean the sum itself to be dependent on $y$!
Hmmmm
 
Yeah, of course
In physics-world, at least, $\int \mathrm{d}x \delta(f(x, y))$ implicitly requires that $y$ have some kind of externally-given value
or so is my understanding
 
3:56 PM
@DavidZ so the indices may be an uncountable number, and therefore the sum is an integral...
 
@DavidZ Doesn't it just yield a function of $y$?
 
@DanielSank Yep
 
@DavidZ Why does $x_i$ have a subscript but $y$ doesn't? Is $y$ standing for some arbitrary number of dimensions here?
 
@yuggib sure, but you can have that in 1D delta-function integrals too
 
@DanielSank In my opinion the only hope is to get a distribution acting on one-variable functions
 
3:58 PM
@yuggib Well, let me explain why I asked this. I have a probability distribution $P(x,y) = (1/r) \delta ( x^2 + y^2 - r^2)$. I want to know the marginal probability of, say, just $y$.
 
@DanielSank because $x_i$ represents a root - a value of $x$ (as a function of $y$) which makes $f(x_i, y) = 0$.
 
@DavidZ Your l.h.s has an integral over $x$ and the r.h.s still depends on $x$, something has gone awry there
 
@DavidZ Oh, $x_i$ is a root... ok.
 
@ACuriousMind oh right, forgot an integral
 
@DavidZ Okay
 
3:59 PM
$$\int\mathrm{d}x\,\delta(f(x,y)) = \int\mathrm{d}x\sum_{i: f(x_i,y)=0} \frac{\delta(x - x_i)}{\partial_x[f](x_i, y)}$$
 

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