The h Bar

bolbteppa

14:04

@0celo7 the pdf math.harvard.edu/~canzani/math253/Lecture11.pdf I linked to yesterday explains why they are the same norm also

@Secret there are a few issues with your calculation above, e.g. the domain is $Q$, the L.H.S. behaves differently on different parts of the domain unlike the r.h.s., the explicit statement of the norm is missing terms

Secret

I have suspected I have made mistakes somewhere, given I am trying to self learn sobolev space from online lecture notes from scratch

bolbteppa

Sobolev spaces are not a standard topic, you only need them if you do math i.e. advanced pde's which, in physics, almost never come up, this is definitely not stuff you should learn until you get your basics down in (a lot of) other areas

Secret

agreed

Danu

@bolbteppa They're like... super standard in mathematical quantum mechanics :P

bolbteppa

Yeah but mathematical quantum mechanics is not standard (and it's a waste of time? :p)

Slereah

14:08

well yes, but how many physicists really study math :p

Secret

If I need to learn them, I believe I will came across them in my quanutm text readings

Danu

@bolbteppa Very much agreed :D

bolbteppa

Quantum mechanics can be done in Hilbert spaces, for the life of me I have no idea where to invoke Sobolev spaces but if I wanted to be pedantic I'm sure I could sneak them in non-stop

yuggib

@bolbteppa Sobolev spaces are Hilbert spaces

Danu

@bolbteppa They're the largest spaces that allow for differentiation if I recall correctly

Secret

14:10

@slereah (don't worry, the answer has nothing to do with the conspiracy) do you think I have the ability to do maths (cause this will be important in years to come when I continue to read my QFT text and raising questions here and elsewhere)?

bolbteppa

Yes

Danu

@yuggib Also that

Slereah

dunno

bolbteppa

@yuggib I explained that last night, you said you read the discussion?

Slereah

You do seem to try to use a lot of diagrams rather than getting down and dirty with the math

yuggib

14:11

@bolbteppa What did you explain?

Secret

@Slereah Well, I have done that, the electromagnetism exercise is an example that filled in part fo the chat yesterday

Danu

btw @Secret the game has much more recent discoveries than the Higgs

bolbteppa

@Secret don't let anyone tell you you can or can't do math, you are an evolutionary being, we're not built for this stuff, you should do all of electromagnetism with pictures (via differential forms em.groups.et.byu.net/pdfs/publications/formsj.pdf haha)

Secret

@danu, cool, I am currently just reached gluons

yuggib

Sobolev spaces are useful in many areas of QM

Danu

14:13

@yuggib But let's face it, very few people are interested in that stuff

yuggib

e.g. non-linear effective evolutions, spectral theory, scattering theory, ....

@Danu :-D not so few...

Slereah

Sobolev spaces in general are useful for DE

Danu

@yuggib Come on :P

Secret

@bolbteppa MTW also have an eggcrate full of these pics, they literally draw the electromagnetic field tensor as an eggcrate and then step their shoes on it so it get squashed

yuggib

@Slereah Actually, for everything that has to do with the Laplacian operator :P

@Danu define few :P

Secret

14:17

More recently, in an attempt to do 0celo7 question, because I have no idea what sobolev space is (thus obviously cannot visualise it) I just start with what we know and then bang through the algebra to hoepfully get the equality 0celo7 want

(that mistake in writing the sobloev norm aside, I am not sure if you will consider I am actually going algebra as I go from step to step)

Slereah

Sobolev space is a function space

probably not best to try visualizing it

Secret

Indeed, analysis itself gave me enough headaches. I prefer abstracrt algebra, at least thigns changes one step at a time

Danu

@yuggib Trying to think of a "norm" ;)

yuggib

@Danu the set of people interested in QM is not a vector space...and probably not metrizable either :P

Danu

@yuggib That's what you think!

Slereah

14:20

Well it's a discrete set

yuggib

@Slereah every set is discrete :D

Secret

$$\int g \phi d\mu=(-1)^{|\alpha|}\int fD^{\alpha}\phi d\mu$$
Well at least all is not wasted effort
Because of today's event, I have learnt what a weak derivative is

While I cannot visualise the above equation, it at least make intuitive math sense to me

Because given a functional acting on some function with compact support $\phi$, $g$ play its intuitve role as a kind of "derivative" because it's action on $\phi$ is the same as if you try to differentiate the distribution $f$ which then scale within the domain of $\phi$

yuggib

in the sense that it is a collection of elements

Slereah

@yuggib what about R!

yuggib

@Slereah R, as a set, is just a collection of objects

the real numbers

Slereah

14:24

no nitpicking allowed :p

Danu

@yuggib Very lame interpretation :P

yuggib

@Danu well, you can give the discrete topology on R, where each subset is an open set

Secret

In the context of physics, one major reason why I tend to visualise maths and try to solve things with diagrams (even though in preactice, I am often the guy in the class that did like 10 pages of algebra in an assignment) is because I am trying to use the maths to teach me the intuition

Danu

@yuggib Very lame topology :P

0celo7

lame discussion is more like it

bolbteppa

14:27

@Secret the motivation for weak derivatives is that, in measure theory, you find you can integrate functions over sets even after you chop out some points which lead to discontinuities (i.e. sets of measure zero). An obvious problem with derivatives is that, at the boundary, you don't have a derivative, thus why can't we set up the notion of a derivative on a set of measure zero? The desire for things to play nice with sets of measure zero means we should use integration to take derivatives,

Secret

indeed, and the equation told me it played its intended role as a derivative looking object

bolbteppa

That's why it's defined that way
https://landonkavlie.wordpress.com/2013/04/06/the-weak-derivative/
http://www.quora.com/Functions-mathematics/What-is-an-intuitive-explanation-of-the-weak-derivative

yuggib

@Danu Why? It is even $T_6$

Danu

@yuggib Exactly: Too simple :P

yuggib

Simple is nice

0celo7

14:33

@Danu nothing can be too simple

for instance, quantum fields are not simple

photon going around a Dirac belt is very simple

guess which one is correct

Slereah

The Dirac belt

duh

I don't think the Dirac belt thing is simple because it's a word salad

Secret

I learnt from spring school that our current best understanding of quantum fields is kinda like a fractal, where for each line you zoom into in the feymann diagram you get another feymann diagram

The professors use this to illustrate the complex virtual gluon sturcture that confines the quarks together within a proton

One QFT book even has its cover designed this way illustrating the fractal like structure

Danu

I definitely would not describe that as our best current understanding of quantum fields

As has been discussed here many times, the Feynman diagrams have little to do with reality, and more with efficient calculations.

0celo7

you killed ACM

idk where he is, but he's dead

Secret

http://www.amazon.com/Introduction-Quantum-Theory-Frontiers-Physics/dp/0201503972

@Danu, I'll keep that in mind

0celo7

14:37

RIP Quantum King

Danu

@0celo7 TL;DR: Semester.

0celo7

oh, school started?

Danu

@Secret Everybody knows that book, @Secret :P

@0celo7 For him, yes.

Not yet for me

0celo7

@Secret that book is also heresy

Secret

to me that book is quite new

0celo7

14:38

it's like 500 pages of Feynman diagrams

and a few hundred of other stuff

Secret

what QFT text you guys will recommend if I am a freshman in QFT

and want to go highly theoretical and rigorous?

Next post contains picture alert, (screenies of my past assignments)

Slereah

classic QFT book is usually like

Peskin Schroeder

Or Quarks and Leptons

yuggib

how much rigorous?

Secret

Slereah

if you want highly theoretical and rigorous, try Weinberg

Secret

14:40

Rigous enough to not be like schurtz

Slereah

I would not recommend making drawings for Weinberg

Secret

ok

yuggib

Weinberg is not rigorous for mathematical standards...

Danu

There exists no really rigorous way anyways

yuggib

but for physical ones is probably ok

Danu

14:42

The closest you can get to rigorous is

Secret

Danu

amazon.com/Local-Quantum-Physics-Theoretical-Mathematical/dp/…

But it will put you completely out of touch with "real physics"

Slereah

>Haag

No you fool

Danu

As in, nobody willl understand what you're on about, and you won't understand any normal research

Slereah

This way madness lies

Danu

14:42

@Slereah My QED course followed it :( So sad...

yuggib

That is just a type of approach

Slereah

Is it the C* algebra method?

yuggib

the algebraic one

0celo7

@yuggib he is pedantic

yuggib

you can get rigorous also in other ways

Slereah

14:43

that is not a very good idea for an introduction

Danu

@yuggib I don't think there are textbooks on other ways, no?

Slereah

Introductions usually are like

yuggib

@Danu yes there are

Slereah

"Hey let's replace E with $d/dt$"

0celo7

yes!

Danu

14:44

@yuggib links plz

0celo7

that's how QM works

Slereah

AND THEN TAKE THE SQUARE ROOT OF KG TO GET DIRAC

yuggib

cambridge.org/ve/academic/subjects/physics/…

Slereah

Also oh no negative probabilities

mb do something

Secret

infinite oscillators -> QFT

that's how they introduce us in the spring school

yuggib

14:45

also, for QFT in statistical mechanics

Slereah

Springs do love oscillators

Danu

@yuggib Does this actually do any real theory?

Like, at least QED?

yuggib

books.google.de/books/about/…

Slereah

Schrodinger wavefunctionals are best

0celo7

interacting bosonic theory

damn mathematicians have invaded again

Secret

14:46

Here's the detail of the spring school I attended:
https://www.physics.unsw.edu.au/events/spring-school-particle-physics-and-cosmology

yuggib

@Danu no rigorous book can do that

without cheating

0celo7

rigor is so highly overrated

why bother

Danu

@yuggib Sure, a little cheating

0celo7

all that matters are the experimental results

Danu

You have to learn QED at some point

Slereah

14:47

QED who needs it

yuggib

@Danu if you want to do perturbation theory, then you are very far from rigorous things

Danu

The point is that you need to learn QFT at some point, not rigorous-model-that-gets-close-to-QFT

yuggib

that's why I said "how much rigorous" in the first place

Danu

But thanks for the reference anyways :D

Slereah

I should get Haag's book

yuggib

14:49

@Danu QFT is fully rigorous, as long as you do consider only some type of dynamics

Slereah

That way maybe I can read Wald's book on QFT :p

yuggib

that, alas, are not the interesting ones

Slereah

QFT in one dimension

QFT in 0 dimensions

yuggib

that is mostly ok

0celo7

qft on a point :O

Slereah

14:50

QFT in 0.5 dimensions

0celo7

what does 1/2 a dimension even mean

Secret

Also (in case you are bothered enough to look at it), the official logical flow of the marking scheme is like this:
1. First, let's assume x >0, therefore we can ignore the absolute sign
2. Next use heisenberg uncertianty principle and do the substitution $x \rightarrow \Delta x and p \rightarrow \Delta p$
3. Then find H when $\Delta x$ vanishes

Slereah

Hausdorff dimension 1/2?

0celo7

what if $\mathbb{R}=V\oplus V$

Slereah

List of fractals by Hausdorff dimension

According to Falconer, one of the essential features of a fractal is that its Hausdorff dimension strictly exceeds its topological dimension. Presented here is a list of fractals ordered by increasing Hausdorff dimension, with the purpose of visualizing what it means for a fractal to have a low or a high dimension. == Deterministic fractals == == Random and natural fractals == == See also == Fractal dimension Hausdorff dimension Scale invariance == Notes and references == == Further reading == Benoît Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman & Co; ISBN 0-7167-1186-...

Hm

0celo7

14:52

then $\operatorname{dim}V=0.5$

Slereah

nothing as low as 0.5

Danu

@yuggib Nonexistent QFT is rigorous :D

Secret

@Slereah Then why I end up having more than 1 page of algebra?

Because in step 1, I felt cheating by ignoring the absolute sign like this, thus I use what I learn in distributions and simply bang through the expression as if it is a maths problem and not dared to make any assumption on the absolute value sign

yuggib

@Danu :D It is a matter of point of view. If you are ok with brutal calculations, you do not need any rigor

and then you get QED, QCD and so on....effectively

Slereah

wot

Secret

14:54

and luckily, because the $|\Delta x|^n$ term is even, it simplifies nicely without any extra assumpetion put in

Danu

Btw guys

yuggib

but what is really happening is still a mystery

Danu

Just in case some of you missed it: The Physics Nobel 2015 is going to Kajita & McDonald for the discovery of neutrino oscillations. It was announced today‌.

2

Slereah

WHEN DO I GET ONE UH?

Secret

The above two screenie is showing when I am getting really dirty with the maths, I just ignore whatever diagram is behind it, bang through the algebra until a sensible result pops up. Only then I start to interpet it

Danu

14:55

SUPERKAMIOKANDEEEE

:D

Secret

This is very different from the picture approach I demonstrate early on in my history on this chat

0celo7

@Slereah get a PhD

Has anyone ever gotten a Nobel in physics who wasn't a PhD

Secret

Slereah

Who knows

Danu

@0celo7 The PhD system is fairly recent.

As a famous example (non-Nobel, though), Dyson doesn't have a PhD.

Slereah

15:01

Well the PhD system dates back to the medieval era

but maybe it wasn't quite as systematic until recently

Danu

@Slereah The PhD system being widely used, then, is much more recent.

yuggib

according to this site, someone got his nobel with the PhD work

0celo7

I only consider Nobel winning physicists to be real physicists

Danu

@yuggib 't Hooft

Slereah

Weren't the people who got the nobel for the CMB just radiodetection operators

yuggib

15:02

(not on the site)

Danu

@Slereah No, Penzias & Wilson were radio astronomers

0celo7

Radio astronomers?

Danu

both had PhD's, too.

Slereah

hm

Maybe we need to look at the most ancient ones

0celo7

Thankfully Einstein is a real physicist

Slereah

15:05

they seem to all have one

0celo7

So get one and publish a monumental paper

Secret

(cont.)
So I can get really dirty with the maths, but nobody is bother to read it because like most of my posts, it's TOO LONG

In fact, a lot of my posts are too long either literally or metaphorically, which is why it is often being ignored

0celo7

That's the case.

Secret

such scenario rarely happens face to face, because there is no "higher reality" they can escape to

Slereah

Well I want a PhD

It's other people who do not want :V

0celo7

15:08

Get your company to pay

Slereah

Apparently "Supersymmetric quantum mechanics an Kahlerian manifolds" was not lucrative enough for my lab to fund

0celo7

Agreed

Do something that increases GDP :)

Slereah

But @0celo7

It was about your favorite theorem

The ATIYAH SINGER Theorem

Secret

While I can think of a way to make my posts shorter literally, I have no control on how to metaphorically make them shorter
Otherwise people won't be overlooking my questiosn that often

yuggib

@Slereah I know people that work on that...but I think they are very few

you should have gone ask them for a PhD ;)

Slereah

15:13

I did but France is pretty shit for theoretical physics

yuggib

you have to think internationally

Slereah

Well yes, I just have to leave my home and country!

yuggib

as at least two of the people chatting now have done :P

and many many others

Slereah

also I graduated like 5 years ago

Not sure they would still want me :(

yuggib

:(

discrimination against age

funny story: I have been told that professors in the US cannot be forced to retire at a certain age (as happens instead in all the other countries I know) because that would be a discrimination against age :-D

Secret

15:17

@Danu Currently on B oscillations

Danu

@Secret I think I've completed the game (up to 2 useless upgrades)

Secret

ok

Higgs boson discovered

Slereah

Again?

did we lose it

Secret

Talking about the particle clicker game

Nice, so they have updated since 2012

wonder what lies beyond...

Danu

@Secret One more thing ;)

Secret

15:28

ok

Slereah

what game is this

Danu

Is it true that the color of objects is mostly due to the first excitation-ground state transition?

Slereah

Danu : It's complicated

Danu

actually that's a dumb question

nvm it

I can assume it is for this answer (I'm writing an answer to the nanoparticle question)

Secret

you cannot have a bare color charge, the strong interaction is TOO STRONG

I wonder if the strong interaction is weaker, what kind of phenomenon can color charges introduce...

Slereah

15:37

The same.

most of the weirdness from the strong interaction stem from the fact that it's non-abelian

Danu

0

A: How is colour difference of CdS nano-particles related to 'Particle in A Box' problem of Quantum Mechanics?

We assume that the reader knows, from elementary quantum mechanics, that the allowed energy levels of a particle of mass $m$ in an infinite potential well (a.k.a. particle in a box) of width $a$: $$ V(x)=\begin{cases}0\hspace{1cm} &0\leq x\leq a\\ \infty &\mathrm{otherwise} \end{cases} $$ are giv...

I'm so tantalizingly close to the Generalist badge

15+ score in 20 of the top-40 tags: I have 15 in 19 of them and 14 in 4 more :P

Physics Meta

0

Q: Flag to post (finally deleted) deemed disputed

Recently I flagged 2 posts by an user named Harsh Raj (a new user, could not find his profile) as one was a spam and the other was of poor quality (includes poor grammar and bad spelling and irrelevant points). The posts were in reply to an answer to this question. Now the first post was flagge...

David Z

chat session coming up! I think I'll be here this time

Danu

@DavidZ Woopwoop! :D

Secret

No pentaquark?

dmckee

15:49

@Secret As long as the strong interaction had the same form it would confine at any strength. It gets stronger as distances increase.

Danu

@Secret Sadly, not

Slereah

I won't for a bit because it's time to go home!

Danu

@dmckee Hey, didn't you have something to do with Superkamiokande at some point?

Secret

ok

dmckee

No. But I did work "just down the mine" from them. KamLAND is in the old Kamiokande facility.

Danu

15:50

@dmckee Okay :)

Alizter

What is the physics chat about?

Danu

You did work on neutrino oscillations though

dmckee

Any way, time to earn my keep. Modern physics is in the house.

Danu

So yay for the Nobel :D

Alizter

Also @Danu How is HSMSE?

Danu

15:51

@Alizter YOu mean... History of Science and Mathematics?

dmckee

@Danu Yeah. KamLAND, Double Chooz, and some of the build on microBooNE.

Alizter

@Danu I didn't look at it for a very long time, only when it first started.

Danu

@Alizter Time to return? ;)

Secret

@dmckee, btw is my qualitative picture/understanding of neutrino oscillation (mentioned yesterday) accurate enough?
While my professor said I can think of it that way, I still felt I am missing out some subtleties

Danu

Activity is picking up a little bit, I think :)

Alizter

15:52

It should get better soon

Good thing I elected you

Danu

@Alizter You did? :P

Alizter

@Danu Yesss

Is there any specific topic for the chat today

Danu

@Alizter Thanks for the support, then ;)

@Alizter Maybe the Nobel prize? :P

Alizter

@Danu Whens that?

Danu

Who of you agree that it's a more exciting one than blue LEDs? :D

@Alizter Announced today

Alizter

15:54

Oh

What happened

Danu

59 mins ago, by Danu

Just in case some of you missed it: The Physics Nobel 2015 is going to Kajita & McDonald for the discovery of neutrino oscillations. It was announced today‌.

Alizter

Nice

Who won Chemistry?

Secret

Question got ignored again...

Danu

@Alizter Announced tomorrow

@Secret Don't be sad :P

Alizter

@Danu OK thanks

So can the Schrödinger equation be thought of as the diffusion equation with an imaginary diffusion coefficient?

Lets discuss

Secret

15:57

@Danu I know that question sounded really stupid, but I really want to check whether I am just overexicted or it is real. Because that professor said this is a valid way to "visualise" quantum mechanical phenomeon

Danu

@Secret I don't know what your visualization was like

Neutrino oscillations are, in some sense, just a linear algebra problem

Just about trying to simultaneously diagonalize two matrices

So I assume it should fit into your visualization program easily

although I've said before that I don't think it's a great program :P

Secret

@danu Below is the "visualisation"

In the spring school, I had a chat with a particle physicists on whether the following way to *qualitatively* think about neutrino oscillation is accurate enough, after being recalled about how the hamitonian evolve state vectors of a state (mixed or pure) in time as it changes the distribution of the observables:

*Picture*
Let’s just for simplicity, assume the three mass states (1, 2, 3) “look” black, white and purple respectively.
Now suppose I have a neutrino source, that fires out a neutrino that initially look whitish. As the neutrino propagate freely away from the source as time prog…

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