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12:00 AM
@ACuriousMind I think vector spaces do carry a canonical smooth structure if we take it to be compatible with the standard one on $\Bbb R^n$!
 
@0celo7 k. Take the maximum norm on $\mathbb{R}^n$. Is that thing smooth?
 
?
 
@0celo7 I don't think it is - if it were, the unit ball should be a submanifold, but the square/cube has those awkward corners...
 
I know
thinking...
 
 
1 hour later…
1:07 AM
@ACuriousMind There's a short story by the name of "Schrödinger's Cat Woman" that involves mostly cats, but a few other animals as well rescued from the thoughtless abuse to which they are put in classrooms the world over.
 
1:33 AM
^ ?
 
1:45 AM
@ACuriousMind What does a duck say about protons? Quark, quark!
 
why
if you were a master physicist I would understand
 
Like "quack, quack!"
That sound ducks make
TIL I learned that Newton's quote "If I have seen further, it is by standing on the shoulders of giants", was a diss towards his rival, Robert Hooke, who was kinda short.
My high school English class teacher clearly overanalyzed the quote.
Just like the people who think Schrödinger was in favor of QM when he came up with his cat.
 
2:03 AM
pretty sure he was
he was saying that the only physical thing in QM is measurement
everything else is irrelevant philosophy
there is no physical meaning to superposition
 
> Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics
Schrödinger's cat is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that may be simultaneously both alive and dead, a state known as a quantum superposition, as a result of being linked to a random subatomic event that may or may not occur. The thought experiment is also often featured in theoretical discussions of the interpretations of quantum mechanics. Schrödinger coined the...
Which cites a paper from Schrödinger
 
thanks for repeating what I just said
(it's obvious you do not know any QM btw)
 
@0celo7 Meh, how much do you consider "any"?
 
I guarantee you cannot state a full set of postulates.
 
@0celo7 I can grasp some of the main ideas of QM
That count?
 
2:16 AM
until you understand the mathematics, no
 
:(
Ah well, I'm looking into it
Regardless, I'd rather spend time learning GR. QM isn't too applicable in space (except things like degenerate gases)
 
properly learning GR is too hard
 
ik. I'm trying to catch up on the maths
 
the physicists are too lazy to write the math properly, and the math people reference the physicists for some stupid reason.
 
Well, if I'm going for a PhD in theoretical astronomy, it's on my list
Considering I'm an astro-nerd
 
2:18 AM
you will not learn GR the way I consider "proper," but I'm not a physicist.
 
So then what do you consider "proper"?
 
Give me a few years
 
ಠ_ಠ
 
My senior thesis might be a rapid, thorough introduction to mathematical GR
there are definitely some folklore theorems in GR I want to formally write proofs for
 
Why are you studying GR?
Aren't you majoring in nuclear engineering?
 
2:20 AM
I like geometry
 
Well then why not be a mathematician
You said you were sick of physics
 
theoretical physics
 
Er...GR is pretty theoretical...
 
I like the mathematical side
no hand waving physicist nonsense
 
But that's most of all theoretical physics
@0celo7 Huh?
 
2:22 AM
@SirCumference you don't know enough math to understand
 
This doesn't seem to be a mathematical conversation
 
what?
 
Regardless, if you hate how physics doesn't provide explanations, why major in nuclear engineering?
 
engineering does not attempt to explain in the way you think physics does
 
You'll end up studying QM or QFT
 
2:24 AM
I'm taking QM right now
QM is not theoretical
 
But you literally criticized it for not explaining where particles come from
 
Where?
 
Long ago
 
I said it's not a fundamental theory
which is true
 
You mean QFT is different?
 
2:26 AM
I don't really care about QFT
it's not fundamental
it's not useful
 
Okay, what's fundamental?
 
no clue
 
What
Do you want something fundamental, mathy or just useful?
 
vtc as too broad
unclear as well
 
"vtc"?
 
2:28 AM
vote to close
common lingo around the "stack exchange"
 
Well, you're criticizing QFT for not being fundamental nor useful
But then you're interested in GR
You're also studying QM even though you are sick of physics
Why not be a mathematician?
 
pure mathematics isn't useful
 
But...nor is GR
In your case
 
which is why I study it in my spare time
 
ok
Well anyway, I'll be learning GR soon enough
That day will happen, 0celo
 
2:31 AM
from what book
 
When you ask me a math question, and I'll answer it
That's the goal
@0celo7 I dunno, whatever book my school gives me
 
what school
 
I'm going to be an astrophysicist
College, maybe graduate school
 
name?
 
We've been over this
 
2:33 AM
I don't remember every conversation.
 
I think I brought it up a while ago, along with my ACT scores. Not something I enjoy doing.
 
 
2 hours later…
4:08 AM
@DanielSank You can get a audio version of the story for free from Escape Pod. Not sure if there is a gratis text version.
It's short and fun.
@SirCumference I trust then, that you will be marrying someone in the for profit sector, right?
That's one of the few fields with worse long-term prospect than particle physics. Especially (in both cases) if you do theory.
 
@dmckee I know. Though I'm not sure if I have any other options
 
I thought @SirCumference was going to be a doctor
 
It's really the only passion I've got
@0celo7 I dunno...
I've also heard that people who get a PhD to be astronomers are really employable in tons of other fields, since they have math and science backgrounds
So that's a plus
 
Then work hard. You really want to be one of the lucky ones.
 
Lucky, as in one of the employable ones, or the profitable astronomers?
 
4:12 AM
the homeless people in front of Union Station in DC are astronomers by training
 
@SirCumference This is more or less true, but not is a way that is good for your blood pressure.
If you can find someone to actually take your training seriously, and if you particular skills are in some sense a match for their needs, then they might interview you.
Once you get it, you've got a path forward, but getting that toe through the door is not easy.
Takes some lucky and a lot of persistence.
 
I know...I've thought long and hard about this. I've never had this much of an interest in any other subject, though.
I'm reading about astronomy on my spare time. I don't have much else I'd be passionate in
I was born with a bad passion.
It could be worse, though. I could've been born with a passion for something like art or acting.
Welp, I'll see where life takes me.
Some of the astronomy professors in my school are literally telling me "Don't be an astronomer if you want to make money. Only be one if you really, reaaallly want to be one."
I'll think it through over time.
 
4:42 AM
sciencedaily.com/releases/2016/08/160825100949.htm Perhaps people might need to start thinking about the Lie algebra of deceit
(For those who are confused on what I am talking about, I am once again hijacking mathematics: Suppose loosely speaking we have an interrogation operator given by the commutator [individual,group], then based on how this research suggests that deceit in group differ from that of individuals, it might be possible that the order of interview matters, which using the hijacked maths will mean [individual,group]=\=0
We also expect the interrogation operator given above may not be actually a Lie algebra, but some more generalised notion of noncommutativity. For example the result of the commutator might be the function of its arguments and violate one or more Lie algebra axioms
 
@Secret why do a lot of Asians seem to do analysis
 
They tend to be good at maths. Another reason might had something to do with finance being one of the most lucrative carriers in Asian countries
Otherwise I am not very sure
 
The analysis I'm talking about is not financial math
Although there seem to be quite a few Asians doing geometry, too
Ricci flow is full of Chinese names
CLN cites 4 different Chengs
CLN are three Chinese dudes
just looking through the biblio
Chen, Cheng, Chau, Chang, Cao, Chu, Ding, Hong, etc.
 
The Chinese do contribute a lot in all science fields in general, you can find Chinese names in other research areas in numbers too. In some sense it is not surprising, back in the ancient Greeks, China already has a lot of scientific achievement from paper to gunpowder and some aspect of astronomy
 
haha, this paper title
"On topological Tits buildings and their classification"
A cup, B cup, etc.?
 
5:02 AM
On unrelated note, the above math hijacking thought have give rise another thought because it mixed with the motivation of defining a covariant derivative. I might experiment myself or ask the QM diff geom guys later on whether you can alway build a commutative operator from a bunch of commutators, and whether such notion is useful
 
sciencedaily.com/releases/2016/08/160825084633.htm Wow, biofuels are much worse in terms of carbon footprint than gasoline?
 
5:28 AM
@Dragonsheep the chat is a bit quiet at the weekends. You might want to try again later today (Monday). I have to say I find maths for mathematicians books deadly boring as for me maths is just a tool and I care only that it works.
 
5:48 AM
@SirCumference Assuming you mean the world outside academia smart people are always readily employable and it doesn't matter what your PhD is in.
 
 
3 hours later…
8:26 AM
what could be the ways of getting into research after school? (if someone knows i want to about research institutes in india)
 
8:53 AM
0
Q: Addition to the flags

WhatAQuestionThere should be a flag to raise complaints like: 1) Lacks research efforts 2) Transfer to Chemistry SE Like this question: How supersonic plan could create shock wave?

 
 
1 hour later…
9:56 AM
@JohnRennie How can you be sure that it works if you don't check it? ;-P
 
@yuggib it works if the predictions it makes agree with the experimental observations. How can you be sure your maths works unless you do the experiments? :-)
 
@JohnRennie That's (theoretical) physics, not mathematics. To be sure that a mathematics statement is correct (works), you have to write the proof (i.e. what builds up a book "maths for mathematicians"). And my question was "how can you use a tool if you don't know it is correct?" ;-)
 
@yuggib And there was me thinking that this is a physics site.
 
@JohnRennie well, that does not prevent physicists to be mathematically pedantic correct :-D
 
 
1 hour later…
11:08 AM
@JohnRennie relatively employable, but the bar is pretty high these days for everybody
 
 
1 hour later…
12:16 PM
@JohnRennie Well, if I do decide to become an astronomer, my only solace will be that I'll earn enough rep on Astronomy SE to match my salary
 
@DavidZ In the UK right now there is a desparate shortage of clever, well motivated workers. If you can't get a job come to the UK. You have until two years after we sign article 50 :-)
 
http://physics.stackexchange.com/questions/277003/weird-light-dispersion
Classical diffraction problem in daily life
 
@0celo7 : who?
 
12:33 PM
@JohnDuffield what?
 
@0celo7 : who's the one person who can distract you away from math?
 
@JohnDuffield Heidi Klum?
 
I don't suppose I could distract you with some physics? You know, some electron articles are absolutely dire. I'm on chapter 7: The electron. And if that doesn't cut it, I'm a tad unhappy because I've broken a cusp off one of my molar teeth. On a bank holiday weekend.
 
12:49 PM
The time travel I have on the previous night has some plotholes because 1) It is from a dream and my dream recall is not photographic memory quality and 2) Dreams have weird logic on how things and causality works, which in the woken world, does not necessary makes sense
caption available shortly
 
Did you just make that
 
nope I made that yesterday, spent 5 hours
 
what on earth am I looking at?
 
A timeline inforgraphic of the time travel story from my dream in the previous night
and I am going to elaborate shortly, (I need to figure out how to type it out in communication channel)
side note: The actual timeline inforgraphic that is constructed within my dream actually look a lot simpler and not very useful
 
@Secret : you cannot travel through time. Sorry.
 
1:00 PM
Well it's dreams, anything can happen in dreams. I am not talking physics here
Closest reconstruction of the timeline infographic saw within the dream
Next, onto the story...
1. (forgot how the dream starts)
 
Nothing happens in dreams. They're just dreams.
 
2. It is now evening and my family and our friend Syria are helping out to prepare a banquet in a pierside restaurant
3. suddenly, there's a burning plate of steak heading fomr the stage onto the rear head of Syria, knocking her out
4. She is later pronounced dead
5. My cousin and I knew exactly what to do, we quickly went outside, where the moon shines bright on the ocean
6. We then hold hands, and raised the other with our palms facing forward and then we started to focus
7. The scene fades into morning. We are now back form a few days ago where Syria have lodged an appication for a police officer role or something
8. We approach one of the policeman which look like this:
and we gave him a paper package. We then waited a few hours.
9. Moments later, Syria happily told us that her application is approved (thus history has changed, because previosuly she failed the application)
10. MY cousin and I then zipped back to the present (actually a few hours later than the time we left). As we peeked through the restaurant window, the mayor is now on the stage and preparing to present an award of execellance for Syria's service to the community (and yes, Syria is alive and well here)
11. 3 days later in the evening, my family went to the tea house to have some supper. There are a lot of high school and primary school students eating there too
 
Anybody want to talk physics?
 
12. To our suprise, the president and his wife are visiting us. Given his reputation, however, this send me and sister into alert
13. The president recognised our achievement (details not revealed in the dream) which is why they want to meet with us to discuss about something
14. The worry of me and sis is confirmed when the students started acting weirdly and camera flashes started to appear
15. No longer can keep my cool, I storm towards one of the students and demand her to delete the photos
 
@Secret Why are you telling us your dream in so much detail?
 
1:14 PM
1) I want to share about it, including the emotions and reactions of the various characters (I have cut away some of the detail already) 2) It's a time travel themed dream, thus some of that might be important in piecing the plot together
It is the emotions of the characters that makes this a bit long winded, if that's what you are thinking
If nobody's interested, I can just stop here
 
Frank Wilczek : "To understand the electron is to understand the world". OK chaps, I've got work to do. Bye.
 
1:33 PM
3) When I typed that dream, all names are actually filtered. I knew that none of them are real which is why I knew when typing them out, there won't be even the slightest chance of the so called awkward situation. For starters, I knew of nobody called Syria, and the internet can freely guess on how many and what type of brothers and sisters and cousins I have because it does not matter what the truth is when it came to my highly personal info
(because the golden rule of the internet is to never ever share highly personla information)
 
1:48 PM
4) One more possibility is I have no idea how to summarise it wthout losing too much important plot points
 
Joke time
Why did the photon go on a diet?
He wanted to stay light!
Wait, photons have no mass, so...
 
Next time if I am going to share a long dream, I think I will just post a link to my blog instead
2
since those tend to be better summarised than the chat version
 
2:33 PM
I have two cars of same mass (2kg) and a spring between (not attached, however). If I release them they will have same speed but opposite direction. And then I do the experiment again and add 1 kg to one of the cars. A book states that in both cases the sum of their kinetic energies will not change. How can this be possible?
 
@PichiWuana The total final kinetic energy has to equal the potential energy stored in the spring.
 
@JohnRennie I don't know anything about the spring. Not the k or the l...
 
@PichiWuana Right, but the energy stored in the spring is the same in the two experiments. All you changed in the second expt was to add 1kg to one of the cars, and that didn't change the energy stored in the spring.
 
@JohnRennie How can we know that that the kinetic energy has to equal the potential energy stored in the spring? And how do we know that the energy stored in the spring didn't change?
I tried to understand it with the fact that $E = U_g + E_k + U_{sp}$ but I don't understand.
 
The KE must equal the PE in the spring otherwise energy isn't conserved i.e. the total energy afterwards would be different to the total energy before.
 
2:52 PM
I understand that the sum of KE of one car plus the PE in the spring will always have the same value (so the mechanical energy of the car will be conserved), but not about the sum of both KE...
 
@JohnRennie taking HF training
this is scary as hell
you can die from 2.5% skin exposure
@JohnRennie HF dissolves glass, how the hell do you store it
 
@0celo7 Gutta-percha
 
@JohnRennie gonna throw Ce in HF and heat to 1700C >:3
in pure oxygen
 
It was nice knowing you :-)
 
> Store in a cool, dry place away from
incompatible materials. HF reacts with many
materials therefore avoid contact with glass,
concrete, metals, water, other acids,
oxidizers, reducers, alkalis, combustibles,
organics and ceramics.
that's like...everything
> Store in containers made of polyethylene or
fluorocarbon plastic, lead, or platinum. Place
storage bottles in polyethylene secondary
containment trays.
who the hell has Pt beakers??
 
3:07 PM
think platinum barrels
 
I want a chunk of platinum :(
What's a fluorocarbon
 
@0celo7 I have a Pt crucible here.
 
It's basically a hydrocarbon with all H replaced by F
Telfon is one good exmaple
Fluorocarbons are extremely unreactive towards even the most aggressive chemcials, because of the strong CF bonds
 
3:23 PM
@Loong we do too
But it's pretty small
 
@0celo7 I still have a small scar from HF. It went through two gloves.
 
@Loong I have to get training because the lab I need to use has HF in it. I pray I never have to use it myself.
 
two good ideas
 
What kind of expt you are doing that need HF besides glass etching?
 
I don't need HF, I just said that.
I hope I never will need it.
 
3:29 PM
@Secret I used it for breaking up of silicate in soil samples. That's actually quite similar to the reaction of glass etching.
 
@Secret It's used for etching certain metals.
e.g. titanium
And zirconium now I think about it. Many years ago I used HF for growing lamellar zirconium phosphate crystals.
 
@Secret HF is used for many things.
 
Hi
Anyone know anything about this reddit.com/r/science/comments/504wwz/… ?
sorry
How can electrons be massless in that material?
Ahh, it mentions something called Dirac Electrons...never heard of them.
 
3:47 PM
@prokaryoticeukaryote Dirac fermions. See for example:
9
Q: How do Dirac fermions arise in graphene, and, what significance (if any) does this have for high-energy physics?

user346Graphene has a honeycomb lattice (in the absence of defects and impurities). By considering the low-energy limit of the half-filled Hubbard model used to model the strongly interacting electron gas we find that the low-energy quasiparticles obey the dispersion relation for massless fermions. Thes...

 
@prokaryoticeukaryote It's a rather strange material called a Dirac semimetal. I'm not sure how accurate it is to call the fermions participating in the conduction "electrons", though.
 
Is there a mathematically tractable, close to ordinary experience example of a system that a exihibits effective particle behaviors. Something we could, in principle, demo in the classroom or on a video?
Effective particle states are not something the non-specialists expects or knows how to interpret, and they are usually grossly misrepresented in the popular press.
 
@ACuriousMind @ACuriousMind too. So, this is clearly above my level of training. It sounds like a dirac fermion is one that is not its own anti-particle. I don't really get the significance of that. Obviously, I get that it not being its own antiparticle should imply several things, which might become more evident if I had more than 2 semesters worth of QM under my belt, but what does this have to do with being "massless"?
 
It's be nice to be able to point at something relatively concrete and say, "No, it's kinda like that."
 
3:58 PM
@Loong Thanks for posting that. I meant to post it, too
 
@prokaryoticeukaryote Nothing, actually. A "Dirac fermion" is just a name for a certain type of fermion, which can a priori be both massive and massless. It just turns out that in these "Dirac materials", conduction happens through states that "look like" the states of massless Dirac fermions.
 
@dmckee What is an Effective particle state? I Googled it but to no avail.
 
Where "looking like" probably probably means the dispersion relation is the same.
@JohnRennie I guess he means what's also called a "quasiparticle"
 
Like a condensed matter Dirac fermion then ;-)
 
Would a crowd with a vacancy moving about be a good example for what dmckee is looking for?
 
4:05 PM
@JohnRennie Yes, I would assume dmckee's remarks are related to the topic being discussed ;)
 
Hm. Well, I had in mind those quasi-particles that become the better (easier, clearer) basis for describing a system. The ones that specialists just start using every time they talk about the system in which they arise. Cooper pairs, phonons, and so on.
Not that I'm at all strong on the subject, but I've seen treatments where these thing arise and are applied.
Only those were at the grad-school level.
 
Well, the chat is a bit short on condensed matter people
 
And in one case the speaker started with "An instaton is a topological soliton." and then launched into paragraphs of discussion which seems to mean something to some of the people around me.
@Secret The trick is to be able to convince your audience that the vacancy behaves—mathematically—like a particle with a mass. That it contributes to the momentum and energy of the system as if it were a particle.
 
A "Slinky spring" level description? Or are you looking for something more advanced than that.
 
I don't know. What are the options? The "An instaton is a topological soliton" guy used a connected-pendulums-with-a-twist model that seems approachable at first, but he quickly headed for high altitude and I lost the thread.
 
4:14 PM
If you are looking for non relativistic, then perhaps the momentum can be represented by how fast the vacancy move about in the crowd, and this depends on how fast each member of the crowd move about. For cooper pairs, I recall back in our uni there was one lesson where two students are assigned in pairs trying to push through a lattice of people. If the crowd is pre arragned with a specific instruction on how to move then it might be able to mathematically ilustrate the interactions of
the quasiparticle with the actual particles
As for energy, I am not sure
 
ANy way. I'm off. Office hours and then my first class of the day.
 
@ACuriousMind We've reached the age when nerds are writing textbooks
ref 544 in Hamilton's Ricci flow:
> Wachowski, Andy; Wachowski, Larry. The Matrix. Warner Bros. Studios and Village Roadshow Pictures, 1999.
 
For solitons, however, we have nice demonstrations like
https://www.youtube.com/watch?v=MADng1fqECY
Vortex rings are also nice demonstrations of quasiparticles (They move about as if they are a particle youtube.com/watch?v=pnbJEg9r1o8
 
4:48 PM
@ACuriousMind are you here?
 
> Well, the chat is a bit short on condensed matter people
The opposite of what's happening in my uni. We have too many condensed matter people and not enough theorist!
 
@ACuriousMind Suppose I have a rep $G\to V$ of a group. Suppose the rep is reducible, and each irrep is an irrep for groups $G_1$ and $G_2$. Is $G=G_1\times G_2$?
 
@ACuriousMind I think this should not be closed.
@ACuriousMind Reporting in.
 
5:12 PM
Dmckee is looking for nice class demonstration of quasiparticles, you have any good ideas on that?
 
5:26 PM
@0celo7 now I am
@Secret There are condensed matter theorists. The two categories don't exclude each other
2
 
O, for that, we only have like 1, thus argument sorta holds
O maybe I should be a bit more specific, we have too many condesned matter experimentalist
so much that the maths part of the physics curriculum suffers quite a bit
We used to have a nonequlibrium stat mech theorist, but he had retired
 
5:50 PM
@ACuriousMind of you could answer my rep theory question that would be great
Although I might have found an easier linear algebra proof that works just the same
 
@0celo7 I'm not sure I understand the question - what do you mean by "each irrep is an irrep for groups $G_1,G_2$"? Are those supposed to be subgroups of $G$?
 
If a group splits as a product, are the projects subgroups?
Products, not projects
@ACuriousMind dammit I mean factors
 
@0celo7 Yes
 
Then they are subgroups but that's what I need to prove
 
Into $A\times B$, you get $A\times\{1\}$ and $\{1\}\times B$ as subgroups isomorphic to $A$ and $B$
@0celo7 Please more clearly state what the given situation is here, then
Where does the representation map on the $G_i$ come from if they are not subgroups?
 
6:08 PM
I'll give you an answer in a bit when I have computer access.
 
vzn
@prokaryoticeukaryote amazing! thx for sharing! there are some aspects of physis that QM is assumed to be able to explain but the precise explanations are unknown/ unmapped. and then there are some phenomena that may be "BSM", aka beyond standard model... have been looking into some theories that link mass with fluid mechanics, but they are very early/ preliminary/ undeveloped at this point...
@Secret wondering why you posted this. reminded me of another remarkable article/ book re drug addiction
@Secret you have a blog? where? when? something to put in your profile
 
In general: I tend to share sciencedaily article that might be somehow related to physics and/or interesting. For this in particular, I am trying to highlight how it might be possible that sometimes we got stuck at problems and overlok something else might have something to do we tend to unconsciously seek for the reward of certain ways of thinking
As for my blog, my wiki is my blog in a sense
for those who want to catch up of that long winded dream (if vanishing any), I have tidied it up here
http://secretuniverse.wikia.com/wiki/The_Time_Travel_Tunneling_Effect_(Story)

(and yes it is long ,it is typical of movie dreams)
 
ok @ACuriousMind
in Mathematics, 1 hour ago, by 0celo7
@BalarkaSen I've had two books say that the property $\mathrm{Hol}_{(p,q)}(M_1\times M_2,g_1\oplus g_2)\cong \mathrm{Hol}_p(M_1,g_1)\times \mathrm{Hol}_q(M_2,g_2)$ is obvious, but when I sit down to do it I get lost
Holonomy groups are defined by representations, so I figured there might be some instant proof of this using representation theory.
What I know is that $T_pM_1$ and $T_qM_2$ are invariant under the action of $\mathrm{Hol}_{(p,q)}$.
So the representation of that group is reducible.
I'm thinking I should be able to block diagonalize the linear map
Then the question is how to show each block is an element of each factor
 
6:27 PM
What do you mean "holonomy groups are defined by representations"?
 
They are defined by the action on $T_pM$
 
I also don't know what your notation means, what are the $g_i$ in the argument of Hol?
 
0
Q: Symmetry transformations, compute infinitesimal change

Marius JonssonI am doing classical field theory. According to Peskin, for the field transformation $\phi \mapsto \phi e^{i \alpha}$ i.e. $f(\phi) = \phi e^{i \alpha}$. That's alright. My problem is that he then goes onto saying for an infinitesimal transformation, the differential is $\alpha \Delta \phi = \phi...

 
@ACuriousMind $(M_i,g_i)$ is a Riem. mfld
 
I wonder if the OP's original calculation is better since it took account of all higher order effects of $\alpha$, or is that not relevant (well I am not very good at taking approximations)...?
 
6:29 PM
@0celo7 I'm not following you - the holonomy group is defined as the subgroup of $\mathrm{GL}(T_p M)$ that you can get by parallel transport along loops based at $p$.
What about this is "defined by representation"?
 
you're defining the group by its action on a vector space, by definition a representation of an abstract group
@ACuriousMind If you know how to prove that above equation, great, I'll gladly forget about this algebra
I'm straying too far from my isle of ignorance
 
@0celo7 That the r.h.s. is a subgroup of the l.h.s. is clear. I have a feeling that you should get equality by considering projecting a loop in $M_1\times M_2$ down to $M_1$ and $M_2$, but I can't see how to show that's a group homomorphism.
 
I agree with your first sentence.
And yes, projecting a loop makes sense.
But how to actually do that is confusing me.
 
6:52 PM
@vzn Which theories are those?
@ACuriousMind So based on your exchange with @dmckee, @JohnRennie, etc, is it correct to say that the "electrons" mentioned in the article are quasiparticles?
In the sense that skyrmions are quasiparticles?
 
What about Skyrim?
 
@0celo7 haha
In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a hypothetical particle related originally to baryons. It was described by Tony Skyrme in 1962 and consists of a quantum superposition of baryons and resonance states. It could be predicted from some nuclear matter properties. Skyrmions as topological objects are important in solid state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch point" singularity ...
 
@prokaryoticeukaryote Yes, although how far they are from actual free electrons I don't know
 
Science reporting needs to do a better job
I mean, why can't they just call them charge carriers, and note that they are electron-like? Why call them electrons?
 
7:28 PM
@ACuriousMind Is it clear to you that $T_pM_1$ and $T_qM_2$ are invariant under the combined holonomy group?
now, we can split the combined tangent space as $T_{(p,q)}M_1\times M_2=T_pM_1\oplus T_qM_2$
so I think an isometry $f\in \mathrm{Hol}_{(p,q)}$ splits as $f=f_1\oplus f_2$
where each $f_i$ acts on one of the tangent spaces
so now you have to argue that each $f_i$ belongs to one of the factor holonomy groups
@ACuriousMind Ok, a loop in the combined space is a product of loops in the factors. So a loop in $M_1\times M_2$ is of the form $(\gamma(t),\lambda(t))$
What needs to happen now is that $f_1$ should depend ONLY on $\gamma(t)$
and $f_2$ depends ONLY on $\lambda(t)$
hmm...
 
7:51 PM
PSA: I was just chatting with a coworker who is a light user of our site. He noted:
> I do notice that a surprising number of the comments basically amount to telling off the asker... not sure what that's about.
This is a very level-headed individual who comes here with the best intentions.
Whether or not this observation is a reflection of anything objective is irrelevant. That this is the first impression gleaned by a cool headed individual is not in the best interests of the site.
 
vzn
@prokaryoticeukaryote particles ≈ solitons/ space ≈ fluid... have some refs/ papers on that. maybe simple place to start is here, have collected many other angles wired.com/2014/06/the-new-quantum-reality
 
@dmckee @Danu @ACuriousMind @DavidZ see previous comment.
Worth keeping in mind. I'm trying to get this person to participate more.
 
vzn
@DanielSank totally sympathize with your efforts to make site more userfriendly, but did you ever read that SE ceo article "sand vs pearls"? think you are fighting uphill battle that is not limited to this SE
 
@ACuriousMind Does parallel transport furnish a homomorphism from the loop group to the isometry group?
Certainly yes
that might be the answer...
 
8:29 PM
@DanielSank That's not particularly useful feedback without knowing more about what constitutes "telling off". Like, if they're talking about comments saying that the question is off topic, does that represent something we should change? Plus, it is just one person's opinion. It's worth keeping in mind only to the extent that it's representative of all our potential new members.
 
@DanielSank I'm not sure exactly why I am being pinged for this :P
Other than that, it's a shame he/she/it sees it that way... I second @DavidZ's comment. What if the person thinks it's rude for us to tell people that their question is off-topic?
 
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