The h Bar

@MarkMitchison I saw a question about operation on fermions. You left a comment but the user wasn't satisfied, and I can understand his objection. glance also tried, but again it's not exactly what the user asked. I thought on the issue and found it problematic. I looked in Ballentine's book, to which the user refers, and I was very displeased with the proof that I saw there. Maybe we can talk tomorrow. It's a strange situation and I don't exactly understand what's going.

user1667423

12:10 AM

Does anyone here have working knowledge of GR?

Mark Mitchison

@Sofia Actually it's not clear from the comment whether the user is referring to my comment or Qmechanic's answer in the linked question.

0celo7

@ACuriousMind loves GR. More than CFT even.

ACuriousMind

Lies, lies everywhere!

0celo7

@user1667423 what's your problem? We can figure something out.

@ACuriousMind You'll be sorry when someone finally quantizes gravity and you have to learn GR.

user1667423

Suppose a toroidal ring of mass is undergoing minor axis rotation

Does this generate a gravitational field going into and coming out of the toroidal ring?

Mark Mitchison

12:12 AM

@Sofia But let's assume that they don't like my answer. In my opinion what they are trying to do is a waste of time and I don't have much inclination to show them how to do it in detail.

user1667423

Sort of like the electromagnetic analogue of gravity (gravitoelectromagnetism) which apparently is a weak-field approximation of GR

Mark Mitchison

@Sofia The best way to manipulate fermions in occupation number representation is taking the anti-commutation relations as a definition, and then writing the states as I did. Any other way is cumbersome and gives little insight.

0celo7

@Sofia @MarkMitchison link to disputed question?

Mark Mitchison

@Sofia "Proving" the anti-commutation relations is an odd thing to want to do; they are part of the definition of the Fermi operators that makes them useful

0celo7

@MarkMitchison That "proof" is the spin-statistics theorem, fundamentally.

Mark Mitchison

12:14 AM

0

Q: Fock Space and fermionic annihilation & creation operators

I have been trying very hard to understand, I am reading Ballentine's book on this topic, but I need help: I realized that I don't understand how many particle states work with the creation & annihilation operators $ C_a $ and $C_a^\dagger $ while trying to calculate $\{C_a,C_b^\dagger\}$. I wi...

I wouldn't call it "disputed".

@0celo7 Well, if you like. Actually what we are talking about has nothing to do with spin. It is just an algebraic definition.

0celo7

@MarkMitchison Sorry, I didn't know the context until now.

ACuriousMind

@MarkMitchison This. There's a reason they're called canonical - they are (more or less uniquely) defining the algebra of creation/annihilation operators.

Mark Mitchison

@Sofia You are right that my comment does not at all answer the question as posed. Rather, I am trying to help the OP avoid wasting their time with a pointless exercise. This is speaking from fairly substantial experience with occupation-number representation ("seecond quantised") calculations with fermions.

Alfred Centauri

@ACuriousMind yep, Ray's pulling our leg me thinks.

ACuriousMind

The entire problem of that user is that Ballentine apparently didn't define the second-quantized notation properly, so there are factors of $-1$ floating around unaccounted for.

0celo7

12:17 AM

@user1667423 I don't understand your question. Any mass generates a gravitational field.

Mark Mitchison

@Sofia But if you want it looks like Chris Drost has actually answered the question.,

0celo7

@user1667423 Do you want to know if it generates gravitational waves? If so, you need to check the quadrupole moment.

user1667423

@0celo7 Correct, and mass currents generate something like a "gravitomagnetic field"

At least that's what I understand

0celo7

Gravitomagnetism is just a parallel between weak field GR and Maxwell's equations.

user1667423

Yep

0celo7

12:20 AM

So, what is your question?

user1667423

I was wondering whether the analogy could be carried over to the example I was thinking about

Basically if you have minor axis rotation of the torus, does this generate a gravitomagnetic field around the torus?

Kind of hard to explain without a picture

0celo7

Is it a vacuum solution?

@user1667423 I'll work under the assumption that it is.

Write $g=\eta+h$. Then $\gamma^{\mu\nu}=h^{\mu\nu}-\frac{1}{2}\eta^{\mu\nu}h^\rho_\rho$

The gravitomagnetic potential is $A_\mu=\frac{1}{4}\gamma_{0\mu}$.

@user1667423 for a vacuum solution, using the Einstein equations, we find $A_i\equiv 0$.

$A_0=-\phi$ is just the Newtonian potential.

The gravitomagnetic $E$ and $B$ fields are defined just as in the Maxwell case.

@user1667423 hope that helps.

@ACuriousMind Soak up the glorious GR.

Unless everything I just said is wrong, which it is.

Crap

ACuriousMind

::soaks in the glorious GR::

0celo7

@ACuriousMind I forgot that the energy-momentum tensor isn't zero inside the torus :'(

It's a ghost torus!

@user1667423 (This is now correct.) If the spatial stresses in the torus can be neglected and the overall field is weak, then you can find gravitomagnetic equations.

Sofia

@MarkMitchison let's talk tomorrow. The use has problem with an anti-commutator for which indeed, I don't see a correct proof. Maybe that anti-commutator rule is correct, but the user showed a problem and he doesn't want to let himself convinced in other ways, he wants to understand what's going with his particular problem. And in his place I would behave the same. So, let's talk tomorrow, can we? Now I go to sleep with no delay.

0celo7

12:33 AM

@ACuriousMind Do you know if $T_{0i}$ is zero for a rotating torus? I wouldn't think so. The system should have nonzero total momentum.

Mark Mitchison

@Sofia Sure we can talk tomorrow if you want.

ACuriousMind

@0celo7 I haven't got the slightest idea.

0celo7

Nigga its a stress-energy tensor

Everyone knows what that is

ACuriousMind

Uh...the variation of the action w.r.t. the metric? :D

0celo7

Even those dumb $U(1)$ CM physicists

(symmetrized) Noether current for translations

Mark Mitchison

12:35 AM

@Sofia As I said, I have no interest in this problem though. If the OP is not satisfied with the existing answers then I don't want to spend more time on it.

ACuriousMind

I have no idea what components of the stress-energy tensor correspond to what.

0celo7

Did you not pay attention in your SR class?

ACuriousMind

@0celo7 Y'see, I already give up at the point where GR has like three different of these damned tensors.

LOL...someone just flagged a dwarf fortress screenshot as offensive

0celo7

@ACuriousMind Well, the stress-energy tensor in QFT is not the same one as in GR.

But they have the same integrals!

user1667423

@0celo7 I'll have to go over these equations. I only have a relatively rudimentary understanding of GR math. Thanks though!

0celo7

12:38 AM

@user1667423 NO

ACuriousMind

I was not lying when I said my GR knowledge is abysmal :)

0celo7

I typed the wrong stuff

Uh, if you want to really learn GR math, check out Straumann. He has a section on GEM.

@ACuriousMind You have 23 GR answers.

ACuriousMind

@0celo7 Yeah, because I can do differential geometry. I know nothing about the physics content of GR, though

0celo7

@ACuriousMind $$P^\mu=\int d^3x\,T^{0\mu}$$ is the total momentum of the system.

Found that one in a QFT book. Boom.

ACuriousMind

Okay, so why should a rotating torus have non-zero total momentum? It doesn't actually move, does it?

0celo7

12:44 AM

@ACuriousMind The guy said "minor axis rotation"

What does that mean?

ACuriousMind

Is the torus allowed to be elliptical? Otherwise I don't even know what a minor axis is

0celo7

That rotation would have momentum.

ACuriousMind

Ah, I see

Yeah, that should have momentum

0celo7

The question is how fast is it going, how big is it, and what do the internal stresses look like?

@ACuriousMind FYI the spatial part of the stress-energy tensor is the stress tensor.

Wait. In physics.stackexchange.com/questions/128475/… you say that the spatial metric could be elliptic.

But an ellipse has nonconstant curvature.

@ACuriousMind I thought FLRW was constant curvature.

ACuriousMind

@0celo7 It's elliptic in the sense of elliptic geometry, not like "an ellipse"

Bad naming, I agree

0celo7

12:58 AM

@ACuriousMind This physics.stackexchange.com/questions/127409/… is damn fine writing.

user1667423

@0celo7 Sorry, by minor axis rotation I meant rotation of the tube itself

sort of like a smoke ring

0celo7

Shouldn't the $\mathrm{N}$ in $y:\mathbb{R}^m\rightarrow\mathrm{N}$ be a $\mathcal{N}$ @ACuriousMind?

user1667423

*rotation of the tube about its minor radius

0celo7

@user1667423 Like a hula-hoop with fixed center?

Timo

hello

ACuriousMind

1:01 AM

@0celo7 Yes, the typesetting of N was not particularly consistent there. Thanks.

Timo

can someone give me a tip how to get answers to my question (physics.stackexchange.com/questions/160927/…)?

0celo7

@ACuriousMind So what you really mean is you don't know any GR phenomenology, right? (Obviously you understand the math.)

ACuriousMind

@0celo7 Yes, I can explain the differential geometry, but I know nothing about the physical phenomena, except that they exist.

user1667423

I'll draw a sketch

cosketch.com/Saved/pITxNDHo

0celo7

@user1667423 does that even work for a rigid torus?

user1667423

1:07 AM

No, it must be flexible

Alternatively you might consider several thin circular rings arranged in the shape of a torus

0celo7

@ACuriousMind Read Hawking & Ellis! Its a differential topology approach to GR.

user1667423

I think the end result should be similar

*rings of mass current

0celo7

Mass current?

user1667423

The arrow indicates the circulation of masses around the minor radius of the torus

I'll draw another picture

cosketch.com/Saved/p3f7hSsK

0celo7

Hmm...interesting. Did you try posting a question?

user1667423

1:12 AM

not yet, I probably will at some point

0celo7

@ACuriousMind Do you know how much complex geometry I need for string theory?

Can I just YOLO it or should I read the section in Jost, for example?

ACuriousMind

@0celo7 Much if you really want to delve into compactifications. Nothing to just understand string theory as such.

0celo7

@ACuriousMind Any chance you know of a book that covers complex geometry really well?

@ACuriousMind Lee doesn't mention Kähler anywhere and Jost only has about 60 pages.

ACuriousMind

@0celo7 No. This time not because I learned it another way, though, but because I don't really know complex geometry specifically, either.

0celo7

::*Looks through Jost*::

ACuriousMind

1:19 AM

E.g. I know nothing about Kähler manifolds

0celo7

What do those :: :: even do

ACuriousMind

Nothing. :: does X :: is just a way of indicating that you are writing in the third person of yourself

0celo7

hermitian metric, holonomic normal coordinates

Cool beans.

$$R=\Delta\log\operatorname{det}h_{i\bar j}$$

If I try to read this book, I'll be on Math.SE every day.

Lol the appendix is a review of Sobolev spaces and elliptic PDEs.

user1667423

From what I can tell, this is what would happen

cosketch.com/Saved/pml9zVCO

0celo7

Tfw school tomorrow. It should snow some more.

@ACuriousMind Do you have any experience with Dine's SUSY book?

I want to attack string theory again, so I'm making a to-read list.

ACuriousMind

1:31 AM

Nope, I haven't read any books on strings/SUSY

0celo7

@ACuriousMind But SUSY is best field theory...

I obtained a (free, legal) copy. I see he has solutions to selected exercises, which is always awesome.

Wow the book lied. He has errata and and one unfinished thing about metastable vacuum SUSY breaking on the website.

Danu

I read "Die Verwandlung" today :)

user1667423

Sorry arrow in the wrong direction

cosketch.com/Saved/pTthwZNH

0celo7

I should have read Fed. 70 but I'm a lazy bastard.

user1667423

Now suppose we increase the minor axis rotation rate over time such that the strength of the induced B field increases over time

ACuriousMind

1:36 AM

@Danu Interesting choice. Most people I know dislike Kafka because they were forced to read him in school :P

Danu

Hah, German-speaking suckazzz

It was interesting

I don't think it's very suitable for high school children

One needs a bit of maturity for it

(which I probably still lack ;D)

ACuriousMind

The high school children fully agree, I think

Danu

It was a good test for my german too

user1667423

Should that not induce a gravitostatic field through the center of the torus?

cosketch.com/Saved/pTNrXJX4

Danu

went pretty well, looked up ~5 words

user1667423

1:40 AM

As would be produced by a theoretical gravitational dipole arrangement

0celo7

Ich muss Deutsch üben. Das ist jetzt ein Deutschland chat.

Danu

Du sollst üben

Or are you really being forced? lol

0celo7

I've forgotten a lot of the nuances.

ACuriousMind

@Danu Most Germans would now call you a pedant :D

Danu

lol

no.

German = pedantic by definition

0celo7

1:42 AM

Was ist QFT auf Deutsch?

Danu

Kwantenfeldentheorie?

ACuriousMind

@0celo7 Just the literal translation - Quantenfeldtheorie

Danu

With a Q?

hah, interesting

0celo7

Das hab ich mir gedacht.

ACuriousMind

@Danu Right. Most Germans would accept you as one of their own after that feat of pedantry ;)

0celo7

1:44 AM

Was ist "gravitoelectromagnetism" auf Deutsch?

ACuriousMind

@Danu Is there any word that actually has Kw in it?!

0celo7

Kwelle

ACuriousMind

@0celo7 Append -us. Done

0celo7

Huh?

OH

ACuriousMind

@0celo7 The word for source is Quelle.

Danu

1:46 AM

@ACuriousMind I assumed because that's what happens in Dutch

0celo7

I would say this is embarrassing, but I don't remember the German word for embarrassing.

ACuriousMind

@Danu Nah, we don't do that, the Kw sound is always written Qu

@0celo7 Das ist peinlich.

0celo7

I promise I used to know German.

I have no idea why I forgot it so quickly though.

ACuriousMind

Seriously, philosophers?

-1

Q: Is knowledge a form of energy?

To better describe my question, do the following experiment: Calculate x=12+26+67+71 Now you might have spent some time in getting the answer. You burnt sugar, you used up energy to get the solution. But due to the conservation of energy, energy doesn't vanish. Where did the energy you spen...

untagged

0celo7

Ich habe meinen Pons Wörterbuch gefunden :)

Does the graviton have a vertex with the knowledge field? If not, then no.

ACuriousMind

1:50 AM

Hmmm:

I'm voting to close this question as off-topic because it's about physics. — Dave yesterday

I could reasonably see some user here cast a VTC as "off-topic because it is about philosophy"

Danu

@ACuriousMind that spoiler though :D

0celo7

kek

Isn't knowledge just some arrangement of neurons or whatever?

Danu

^do you spend time on 4chan?

0celo7

Possibly

ACuriousMind

@Danu It doesn't do much to raise my confidence in philosophy, at least :D

Danu

1:54 AM

depends on the definitio nof knowledge

ACuriousMind

As always, my favourite webcomic provides an excellent summary of the Gettier problem of knowledge.

0celo7

@ACuriousMind There's different types of philosophy. "I'm high as fuck philosophy" and "how should we run the world" philosophy.

This is the former.

That girl is an objectivist. The father is a "high af" philosopher.

@ACuriousMind Does anyone study probability in QFT? Fields aren't wave functions.

ACuriousMind

@0celo7 You can associate wavefunctional to states and pretend you're just doing QM for a long time. Also, all scattering amplitudes are just probabilities, after all.

For indications of a deep connection between the nature of quantum vs. classical probabilities with the (non-)commutativity of observables, see this answer

Danu

No, they're inverse areas :D

0celo7

"Also, all scattering amplitudes are just probabilities, after all." Yeah, Ok. Speaking of, I've heard that QM is a (0+1)-dimensional QFT.

How do we get position if we have no position variable?

Danu

2:01 AM

Think about the Feynman path integral

ACuriousMind

@0celo7 You treat position as the field - QM is the theory of the position field $x(t)$

Danu

in the feynman path integral it's kind of clearer

0celo7

Makes sense.

ACuriousMind

@Danu Shush. $\hbar = 1$.

Danu

just see what the action of a 0+1-dimensional field theory looks like

ACuriousMind

2:02 AM

Also, "whatever other unit I have to set to 1 to make my previous statement true" = 1

Danu

@ACuriousMind ...h=c=1 will not help you here, will it now

length$^{-2}$

ACuriousMind

Ach, damn

0celo7

@ACuriousMind Please settle this once and for all. Can we derive the SE from first principles?

Danu

No

0celo7

Why not?

Danu

2:02 AM

Well, not without educated guesses

because it's physics, not mathematics

it totally depends on what you mean by 'first principles'

0celo7

So where exactly do we take the leap of faith?

Danu

I think the way it's typically derived in e.g. Sakurai is pretty first-principles

0celo7

Page? I haven't read the whole thing.

ACuriousMind

There are so many different "derivations" of the SE that it is impossible to say what exactly we have to assume

Danu

Chapter 2, first section (page ~66)

up to 2.1.25 which is the SE

0celo7

2:06 AM

Yeah I see. That's the way Ballentine does it, too.

ACuriousMind

(Also, I think the SE is not the best thing to think of as the fundamental equation of QM. Heisenberg's equation of motion is so beautifully close to Hamilton's classical equation of motion that I find the Heisenberg picture much more natural to derive.)

0celo7

I guess the assumption is that $H$ is the energy operator?

ACuriousMind

"The Hamiltonian is the generator of time translation" is also classically true.

0celo7

@ACuriousMind Doesn't that require the assumption PB -> [.,.]

ACuriousMind

(which is equivalent to "The Hamiltonian is the energy")

Danu

2:07 AM

@ACuriousMind It just seems the Heisenberg picture is total crap for computations lol

0celo7

@ACuriousMind So no assumptions then?

@ACuriousMind Do you have Sakurai?

Danu

Unitarity

ACuriousMind

@0celo7 Well, you are not really adding an assumption if you just take classical things to be still true quantumly, eh?

Danu

In some sense you do

ACuriousMind

I mean, if you were satisfied classically to have the Hamiltonian as the energy observable, you have no reason to doubt it quantumly

0celo7

2:09 AM

@ACuriousMind Yes you are.

Danu

unless you keep everything, but you don't

so you still have to specify which things to keep

the question is, how concisely can you specify it

@ACuriousMind This is so naive!

ACuriousMind

@Danu But you keep the entire structure of the observables

0celo7

Aharonov-Bohm is false classically. Therefore it is false quantumly too.

ACuriousMind

@Danu Hah, yes, it is - but I see rather that the assumptions added are the things different from classical mechanics, not those that are the same

Danu

@ACuriousMind Then maybe you should have some statement about the algebra of observables remaining the same or something

ACuriousMind

2:11 AM

@Danu Yeah, the rigorous procedure is geometric quantizatiion and highly tedious because it takes ages to get something that resembles a Hilbert space structure out of the phase space

0celo7

So we can strongly motivate the SE by demanding unitarity, hermiticity and the Hamiltonian being the energy operator?

Danu

@ACuriousMind And even that is not entirely "waterproof", or so my LMU professors say

damn it's late

ACuriousMind

@Danu The are some issues lurking that you cannot be entirely sure that what you produced is actually always a Hilbert space or something like that.

Danu

I should go to sleep

0celo7

I don't like how Shankar simply says it cannot be derived and doesn't even try to motivate it.

Danu

2:13 AM

we, @ACuriousMind, haha

@0celo7 Lol you should have a look at Griffiths :D That's a terrible start to a really nice book

ACuriousMind

@Danu It's only 3am :P I've not even been awake for twelve hours yet

0celo7

Is Griffiths worth reading?

Danu

Jesus, you sleep in that late?

@0celo7 Only if you don't know any QM yet

0celo7

I've read Shankar cover-to-cover, parts of Sakurai and parts of Ballentine

Danu

Don't read Griffiths

total waste of your time :P

way too easy

It'd be like repeating Shankar

@ACuriousMind I typically get up before 10 AM

although last morning I only awoke a minute before it was over

which was nice: Finally getting dat holiday sleep rhythm

Now, I will proceed to listen to the Sleeping Tapes

ACuriousMind

2:16 AM

Nah, if you let me sleep, I'll typically go to sleep ~6am and sleep till ~2-3pm

0celo7

My to-read list: Kaku QFT, Georgi Lie Algebras, Dine SUSY, Polchinski + Becker, Becker & Schwarz

Danu

Why would you waste time with Kaku?

I've never heard anyone recommend it

0celo7

I liked the first chapter!

It's not a Feynman diagram fest like P&S

Danu

Have you looked at Banks, Brown?

0celo7

No

I will now

Danu

2:17 AM

Or Bogoliubov if you wanna kick it old school

(don't actually do that)

mathim.com/joinmeinhere

0celo7

I don't want to read a book if I can't pronounce the author's name

What is that link?

Danu

You'll have to learn how to pronounce Bogoliubov anyhow: He's very important (e.g. in QFT in curved spacetime)

ACuriousMind

@Danu You really think anyone on the internet is gonna click a link that says join me in here?

0celo7

I did.

ACuriousMind

I'll be disappointed if there isn't Rick Astley behind that link.

0celo7

2:19 AM

Not the smartest.

HDE 226868

I'm not, either.

Danu

@ACuriousMind lmao

@ACuriousMind Sorry to disappoint

user54412

@user1667423 Since the mass distribution is stationary, the quadrupole moment is independent of time. Therefore there are no gravitational waves. There should, however, be a frame dragging through the center, as you've drawn it.

user54412

You could imagine a bunch of point masses all rotating in the sense as you've drawn

user54412

Each one induces frame dragging as seen in the Kerr metric, and all the effects should add

user54412

2:31 AM

I suppose gravitomagnetism would give you the result more quantitatively, but honestly that's just a mess of equations, so I prefer to think about these things intuitively.

user54412

@ACuriousMind The philosopher in me is really disappointed, because a good philosophy community could have handled this just fine. The premise is logically flawed: If A is conserved, and we think A diminished, and we observe B increased, clearly B is A. I mean, that just doesn't make sense.

user54412

Fumbling something so simple is what gives philosophy such a bad rap

ACuriousMind

^fully agreed. I'm baffled they evidently closed this question as being about phyiscs.

Kyle Kanos

@ACuriousMind They saw "conservation of energy" and stopped thinking about the problem

ACuriousMind

@KyleKanos So, uh, I am not allowed to discuss scientific concepts in philosophy?

Danu

2:38 AM

@ACuriousMind non sequitur?

Kyle Kanos

@ACuriousMind It seems that is sadly the case

Danu

Oh lol like that

never mind me :)

user54412

@Danu non sequitur? :)

Danu

I really should go sleep

@ChrisWhite I had that one coming

ACuriousMind

I mean the question "Is knowledge energy?" is not something I'd really want to see as a philosopher, either, but it is definitely more philosophy of knowledge than physics

user54412

2:41 AM

Random aside: The hardest thing about GR simulations is plotting the data that comes out of them. Seriously, it's almost like plotting packages were designed by people who don't transform their coordinates at the drop of a hat. And they always assume time is some global parameter that never mixes with space.

Kyle Kanos

@ChrisWhite Why would time mix with space :D

Danu

Oh god, not this again

you 3-dimensional being!

user54412

Indeed. Probably because time is energy and energy is knowledge

user54412

Actually, today I realized how awful my data dumps really will be. Everyone likes to plot black hole stuff in Boyer-Lindquist coordinates. But the right way to simulate black holes is with horizon-penetrating coordinates, which will have different surfaces of constant time from B-L.

user54412

So I have to dump a whole sequence of time-slices in code coordinates in order to construct a B-L time slice

Kyle Kanos

2:45 AM

3

Q: Numerical relativity coordinate system displayed

In a picture or video of a numerical relativity simulation, such as a neutron star merger into a black hole, how do they set up their coordinate system? Lets take the point in a video corresponding to x=10km, y=20km, z=30km, t=1ms. Spacetime itself is distorted, in a very complex way, so how do y...

general-relativity simulation

@ChrisWhite IMO: requiring post-processing is not a big deal

Sabre Tooth

6:54 AM

Category 4 cyclone bearing down here, so any random pings may have to wait - survival is a bit more important - I know that would be a shock to some

infinitesimal

Take care @SabreTooth

Eka

8:44 AM

Can any body tell me the difference between nature letters and nature articles published by nature magazine. Are they both the same or different publication. If different where can i get nature letter archieve. This is a link to one nature letter article nature.com/nature/research/research_by_type.html

Sabre Tooth

9:20 AM

cat 5 cyclone now....

Neuneck

9:37 AM

@Eka I am not entirely sure about Nature, but several Physics Journals also have a "Letter" issue, where only very short articles presenting an idea are published. So in Phys.Lett.X you will not find articles with 20+ pages, while Phys.Rev.B will also allow articles with 70 and more

alarge

10:07 AM

@Neuneck Phys Lett and Phys Rev are different journals by different publishers (Elsevier, APS, respectively). Phys Rev has, as its most prestigious publication, Phys Rev Lett, which only allows for short publications, Letters. Note though that many of the others in the Phys Rev family have "Rapid Communications", whose length is also restricted.

From what I remember, Nature publishes both Letters and Articles and the former is one page shorter (I think the limits are 3 pages and 4 pages, respectively).

Sofia

@MarkMitchison Mark, if you say that "Proving" the anti-commutation relations is an odd thing to want to do; they are part of the definition of the Fermi operators, then I'd like to learn a bit from your experience. I didn't have much to do with fermions and the anti-commutation relation, and I am quite worried with a strange thing that I saw there. Different proposals that I saw to overcome the problem, do not actually succeed to do so. So, if we can talk, I would be glad.

Neuneck

@alarge Dx major misconception on my part. That's what you get from always reading the arxiv version and picking quotes in the bibtex format from inspires.

alarge

@Eka Here are Nature's guidelines. So it's 4 pages for letters and 5 for articles.

infinitesimal

2

Q: Two severe cyclones connected by a monsoonal trough

At the time of writing, areas around the Northern Territory (TC Lam) and Queensland (TC Marcia) in Australia are in the path of severe cyclones (category 4 at the moment, with the Queensland one - TC Marcia predicted to reach category 5 - Category scales used for Australia and Fiji). These cyclo...

meteorology severe-weather

3 hours ago, by infinitesimal

Take care @SabreTooth

Neuneck

@Sofia If you construct a theory with Fermions and demand that the field and its conjugate momentum fulfill a commutation relation you will find that the spectrum is not bounded from below. This is also apparent in the Dirac equation, where people sometimes argue with a "Dirac Sea" in which all negative energy states are filled so that the Pauli exclusion principle bounds the spectrum.

Sofia

10:18 AM

@0celo7 This is the link. I am sorry it's only now that I saw your message.

@Neuneck I don't have enough experience with fermions. I have a problem with an anti-commutation relation which seems simply not true. I saw a proof which is taking people as fools and since the anti-commutation relation is one very often used, I would like indeed to clarify it as much as we can, and if we cannot I'll consider to apply to some specialist.

Neuneck

@Sofia What do you know about Fermions? Is this a specific anticommutation relation you're talking about or anticommutators in general?

Sofia

@Neuneck it's the $\{ C_a C_b^{\dagger}, C_b^{\dagger}C_a \} = \delta_{a,b}$. A frequently used relation.

@Neuneck if $a \ne b$ we should have $C_a C_b^{\dagger} = - C_b^{\dagger}C_a$. Well, it seems not true.

@Neuneck if you try to apply the operator $C_a C_b^{\dagger}$ to the state $|a>$, and if you try to apply $C_b^{\dagger}C_a$, you'll see that you don't get the same result just differing by a minus. What you get in the first case is a complication.

Neuneck

10:40 AM

The important thing when dealing with fermion states is to stay veery careful about the order of operators and what exactly you are doing.

The operators are defined through their action on the vacuum state

$C_a \ket{0} = 0$

$C_a^\dagger \ket{0} = \ket{a}$

and the anticommutator ${C_a, C_a^\dagger} = 1$

that's all you can use

So $C_a C_b^\dagger \ket{a} = C_a C_b^\dagger C_a^\dagger \ket{0}$

From which you get $ - C_b^\dagger C_a C_a^\dagger \ket{0}$ since C_b^\dagger and C_a anticommute

then you go on to $- C_b^\dagger * 1 \ket{0} + C_b^\dagger C_a^\dagger C_a \ket{0}$

which gives you $-C_b^\dagger \ket{0} = - \ket{b}$

and $C_b^\dagger C_a \ket{a} = C_b^\dagger C_a C_a^\dagger \ket{0} = C_b^\dagger (1 - C_a^\dagger C_a) \ket{0} = C_b^\dagger \ket{0} - 0 = \ket{b}$

so $C_a C_b^\dagger = - C_b^\dagger C_a$

which just sais that C_a and C_b^\dagger anticommute

Mark Mitchison

11:32 AM

@Sofia As I said, Chris Drost has already answered the question you are interested in.

Danu

12:10 PM

@Neuneck Not only this, but the fermionic fields will even violate causality!

Neuneck

@Danu Neat! Is there an easy way to show that?

Danu

Yeah, just try to impose commutation relations and work out the commutator $\delta(x^0-y^0)[\Psi(x),\Psi^\dagger(y)]$. It will not be proportional to $\delta^3(\vec x - \vec y)$

In fact, you can do this 'in tandem' with the anti-commutator derivation

the derivations are identical until right at the end

0celo7

12:43 PM

dat two hour delay

@Danu Zeidler defines the Laplace transform with a complex exponential. Is that some German thing?

Also instead of $(-\infty,\infty)$ he writes $]-\infty,\infty[$

And he insists on calling the Dirac delta a function, even in the chapter on distribution theory!

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