The h Bar - 2017-03-17 (page 2 of 6)

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10:10 AM

1

Q: Is there a topological difference between an electric monopole and an magnetic monopole?

When we introduce magnetic monopoles, we have duality, i.e. invariance under the exchange of electric and magnetic fields. Magnetic (Dirac) monopoles are usually discussed using topological arguments. The electromagnetic field is infinite at one point and thus we restrict our description to $...

quantum-mechanics electromagnetism differential-geometry topology magnetic-monopoles

Sure, you can describe a magnetic monopole as a gradient of a magnetic scalar potential, but that (for reasons I read 6 years ago thus forgot), therefore it does not work

6

Q: can one introduce magnetic monopoles without Dirac strings?

To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization of charge. Okay, it looks great. But is this the only way to introduce magnetic monopoles?

magnetic-monopoles maxwell-equations dirac-monopole dirac-string

and then, I forgot why we must need a real valued 4-vector potential and cannot just have some vector field that has a curl and divergence part as it can always be done via helmhortz theorem

Trying to work out all of this is not going to be a back on an envelope calculation

Shoshichi Kobayashi

Shoshichi Kobayashi (小林昭七, Kobayashi Shōshichi, born on January 4, 1932, in Kōfu, Japan, died on 29 August 2012) was a Japanese mathematician. He was a brother of electrical engineer and computer scientist Hisashi Kobayashi. His research interests were in Riemannian and complex manifolds, transformation groups of geometric structures, and Lie algebras. He graduated from the University of Tokyo in 1953. In 1956, he earned a Ph.D. from the University of Washington under Carl B. Allendoerfer. His dissertation was Theory of Connections. He then spent two years at the Institute for Advanced Study and...

@Slereah dork ?

you met him or what ? :D

→ 1 message moved to Trash

@Slereah be nice

lol :P

@JohnRennie Why does taking waves as vectors and adding them to find resultant using parallelogram law work? (when they have same angular frequency) My textbooks uses the method of assuming waves to be vectors quite frequently but doesn't give any proper explanation. Do you know the reason as to why that technique is valid?

I mean equations of the form $A\sin(wt-kx)$

10:32 AM

Hi

@2017 it depends what the wave is. Some waves are vectors, like light, and others are scalars, like sound.

Do primary valencies are always negative ions ?

Coordination compound

@2017 Do you mean adding waves that have different phases?

@JohnRennie Yeah, right...I meant plane progressive waves...

or even light waves

Like when we have to add waves like $A\sin(wt-kx) + A\sin(wt-kx +\phi)$

We assume the waves to be vectors of magnitude $A$ and tilted w.r.t. each other by angle $\phi$

then apply parallelogram law

I'm still unclear what you're asking because you could be asking two different things:

1. you could be adding two waves that are polarised in the same plane but have a different phase

2. you could be adding two waves polarised in different planes

Which is it? Your expression $A\sin(wt-kx) + A\sin(wt-kx +\phi)$ is adding two waves polarised in the same plane but with a different phase.

10:40 AM

@JohnRennie Yes that one, in the same plane!

OK. A wave has two components - the amplitude and the phase. And it's convenient to represent the wave by a complex number $\psi = A e^{i(kx - \omega t)}$

So when you add two waves you are simply adding two complex numbers.

@JohnRennie Okay, right! Then ?

OK so far?

yes

But complex numbers are vectors on the Argand diagram. So when you add two complex numbers this is equivalent to adding two vectors.

10:43 AM

@JohnRennie Ohhhhhhh!!! I see now...I should have thought of it as complex numbers....now it makes sense!

The phase is just the angle between them

the two complex numbers

Yes

thankewww :D

11:14 AM

user image

who exactly is this guy?

MathFoundations119: Mathematics without real numbers

> Real numbers will go the way of toaster fish; claims of infinite operations and limits will be recognized as the balder dash they often are; and finite, concrete, write-downable mathematics will enter centre stage.

Well, he being an ultrafinitist I can understand he want to throw away infinities, limits, cauchy sequences and so on, but imaginary numbers? those are not even infinite to begin with

@JohnRennie What the hell is a toaster fish?

user image

11:19 AM

@ACuriousMind Don't know, but it sounds like food so it gets my vote! :-)

Consensus on the Internet seems to be that Wildberger isn't a crank. He's a competent mathematician but chooses axioms that are non-mainstream.

Which is a perfectly reasonable thing for a mathematician to do.

You can do that and still be a crank

I actually chat with him back in my 1st year, I do find his rational trigonometry quite useful to knocking down annoying x ray crystallographic calculations in a lattice structure

because all the trig becomes surds, thus very easy to handle

@Slereah Ok, he's no madder than most mathematicians - which isn't saying much

@JohnRennie He does claim that the other axioms "don't make sense" - my problem with him lies less in the mathematics he does but in the way he dismisses what other mathematicians do.

And no physicist has ever dismissed the views of other physicists as nonsensical :-)

user228700

11:25 AM

Oh God Why...

user228700

Pi Day 3/14/2017 - Venn Piagram

@ACuriousMind I didn't say he was a nice man :-)

@Kaumudi.H Wut

user228700

@JaimeGallego Apricots, blueberries, salmon and trout; you tell me.

Surströmming would be lovely with that!

11:29 AM

@Kaumudi.H That's ... erm ... I'm lost for words. And that doesn't happen often.

@JohnRennie No, I don't think that's what he does. He literally says "we are being mislead" by mainstream mathematics.

Ok, I'm not qualified to comment.

user228700

@JohnRennie I too, Sir, am totally lost for words .__.

16 mins ago, by Secret

Well, he being an ultrafinitist I can understand he want to throw away infinities, limits, cauchy sequences and so on, but imaginary numbers? those are not even infinite to begin with

O wait sorry, I read the wrong thing

He only killed the continuum (the reals and other uncountable sets), not the complex numbers

@Kaumudi.H The pizza with the fish looked particularly gruesome.

user228700

11:37 AM

I wonder if she took a bite...

0

Q: Why is my question on hold, flagged as homework and why the downvote?

I have a question about my Physics Stack Exchange post: Shankar Quantum Mechanics: Proof Inverse Of Operators Hi! I don't get why my question was flagged as homework plus a down-vote. It is not meant as homework. Also, that line beneath the imgur link was my (poorly?) proof, In the footnote...

discussion closed-questions homework specific-question

I doubt it - would you? :-)

user228700

Absolutely not, for several reasons besides that it looks hideous!

user228700

However, she might not be totally crazy after all:

user228700

user image

user228700

11:39 AM

Phew :-)

Peach and blackberry ...

user228700

STILL BETTER THAN PUTTING FISH ON IT.

True :-) Though that isn't saying much :-)

I have two pizzas in the freezer. I wonder what a fish pizza would be like.

user228700

@JohnRennie Please don't. For the love of all things bright and beautiful.

2

@JohnRennie Pizza tonno is perfectly normal, isn't it?

11:43 AM

Whale pizza? For when I'm really hungry?

@ACuriousMind Seems like a waste of good tuna, but each to their own.

Well, but it exists, so putting fish on pizza is not that unusual

Sardines on pizza are also not unheard of

foodtolove.com.au/recipes/mediterranean-sardine-pizza-9921

user228700

...although, it sounds only as bad as chocolate on pizza, which is sadly, something I've subjected myself to :'-(

I never did try the chocolate pizza. probably as well.

user image

user228700

11:47 AM

@JohnRennie Yes. Good on you! :-P

I did eat shrimp pizza once. It doesn't really go well with the pizza bread...

Hmm, prawn cocktail pizza?

@JohnRennie cocktail ? :P

You should try a spider pizza or rabbit pizza :D

Prawn cocktail, also known as shrimp cocktail, is a seafood dish consisting of shelled, cooked, prawns in a cocktail sauce, served in a glass. It was the most popular hors d'œuvre in Great Britain from the 1960s to the late 1980s, and was likewise ubiquitous in the United States around this time. According to the English food writer Nigel Slater, the prawn cocktail "has spent most of (its life) see-sawing from the height of fashion to the laughably passé" and is now often served with a degree of irony. == Origins == A dish of cooked seafood with a piquant sauce of some kind is of ancient origin...

user image

(I wish they were real)

11:51 AM

No you don't

@JohnRennie Ah, looks tasty!

Dec 3 '16 at 15:48, by John Rennie

user image

We know ;P

Damn :-)

lol, you didn't need to delete that

Hey ACuriousMind, would you happen to know the following

11:54 AM

Yes, "the following" is an English phrase to denote that which follows :)

Anyone would think it's Friday ...

I have an oriented, Riemannian manifold of dimension $4n$ whose holonomy reduces to a subgroup, namely $Sp(n)Sp(1)$, which is not $Sp(n)\times Sp(1)$, but just the subgroup of $SO(4n)$ you get by embedding the symplectic groups into and then taking products of these two subgroups. It's isomorphic to $Sp(n)\times Sp(1)/\Bbb Z_2$ since $(\pm id,\pm id)$ are identified.

Now, my question is:

The tangent bundle is associated to the $SO(4n)$-principal frame bundle via the fundamental representation right? Since [something something reduction theorem] I may reduce the frame bundle to an $Sp(n)Sp(1)$-principal bundle $P$, I get an induced representation. Which is it?

It should be the fundamental representation of $Sp(n)Sp(1)$ right? A paper I'm reading asserts that it is the tensor product of the fundamental representations of $Sp(n)\subset U(2n)$ and $Sp(1)\subset U(2)$.

@Danu Uh, that's purely group theoretical - you have to investigate the fundamental of $\mathrm{SO}(4n)$ for which reps of that subgroups it splits into.

So I'm asking if you know how to do this :p

I don't know the representation theory of $\mathrm{Sp}(n)$, sorry.

Otherwise the first thing would be to look at what its Casimirs are mapped to in the SO(4n)-representation

11:59 AM

sigh

I'm not at all knowledgeable about representation theory :\

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