In my textbook, it states that a nonholonomic basis is the basis used by a physical observer, representing a basis w.r.t a local Lorentz frame.
Conversely, a coordinate basis represents the global spacetime.
Can someone explain why this should be so?
My current thoughts are that for a physical...
@ACuriousMind the last line in the top answer, about being able to pick a co-ordinate basis or anholonomic one, is this related to what you were saying about the spin connection at all?
@naturallyInconsistent I figured out the answer I was looking for for my (admittedly not so well phrased) question last night
I wanted to understand where the "Average interaction" came into play in the HF equations
I realized the answer when I compared the HF hamiltonian to the regular hamiltonian. While the regular hamiltonian has $1/r_{ij}$, the HF hamiltonian has the coulomb and exchange integrals, which express an average over the entire wavefunction
That does not tell us the difference; as far as I currently understand of your wording, those are exactly the same Hamiltonian, just approached with different ways to solve for the wavefunctions?
Although I suppose you could say its not a Hamiltonian in the usual sense because its eigenvalue doesn’t represent the energy of the system, it double counts the electron electron interactions
@Allie I think you have correctly noted that the HF Hamiltonian has Coulomb and exchange operators between the electrons; but I'm confused as to why you think these are different: The $1/r_{ij}$ in the "regular" Hamiltonian, immediately imply the Coulomb operator, and the Slater determinant causes the Exchange operator to appear from there.
?? If you have done it before, then you should know that they are the same thing, just that the J K form summarised it in a way that is easier to talk about.
there's no way. because they have different expectation values for the slater determinant you get out of HF
if you do $\langle \Psi_0 | \hat{H}^{HF} | \Psi_0 \rangle$ where $\hat{H}^{HF}$ is the HF Hamiltonian, you get the sum of the orbital energies (eigenvalues of Fock operator) which is not the same as the expectation value of the "regular" Hamiltonian. it double counts the coulomb and exchange interactons
besides, if they were the same Hamiltonian, the solution to the HF equations would be the exact ground state energy
Oh, this is a very idiosyncratic exposition, but I suppose it has a point. The issue is that usually people would not be computing individual orbital energies in the first place, partly because of the reason that the text is discussing. Kinda that this is a trivial result. Which is why I was assuming that you werent discussing this trivial result.
is the HF hamiltonian just the sum of the fock operators or not?
Besides, when you diagonalize the Fock matrix, you obtain the eigenvalues of the Fock matrix, and you have to compute the one-electron part of the Hamiltonian to add it to those eigenvalues in order to get (twice the) expectation value of the regular Hamiltonian
which is how HF gives you a ground state energy according to this book
I dont rerally understand what you mean by "trivial"
@Allie I dont know what you mean by "sum of the Fock operators". I don't think the usual presentation would have individual orbital energies being presented; we would calculate this, and we would also sum them, but it is definitely known that the individual orbital energies are pretty much nonsense and would not be presented at all. Or maybe in the code they could just halve the contribution of the J and K terms, so that the sum is automatically correct.
Tetrad is literally vierbein (tetra is Greek for "four"), the arbitrary-dimensional version is the vielbein, which is also sometimes still called tetrad by people careless about etymology
@handan_toddler I don't know enough about philosophy to comment.
I concede that philosophy of science plays an important role in keeping us physicists honest, by and large I consider philosophy a harmless passtime but of little importance in real life.
I have no problem with my taxes paying the (basically trivial) amount needed to fund philosophy departments, but that's similar to my view on the arts like opera or painting. They all make the world a more interesting place but from a utilitarian perspective they are mostly pointless.
@Slereah So did Mein Kampf or many other books that I wouldn't class as philosophy.
"Why can't you be like the math department, who only needs funding for pencils and erasers, or like the philosophy department, who doesn't even need erasers!"
Marx and Engels were kind of a weird pick to choose as their dogma really
Like they wrote a bunch of things that we would probably consider as unrelated to politics and those were also considered very important in the soviet union?
I'm not sure enforcing the idea of dialectic materialism was that important to the whole enterprise
i think philosophy is an art and art has utility. art is the only thing in the life that has utility once one has satisfied food and water and security needs @JohnRennie
the utility of physics in itself is also as an art @JohnRennie
Which is why I have no problem with my taxes funding philosophy departments. Though I'm also fine with funding social care so I imagine many will dismiss my views as those of a worthless communist.
@qwerty When I worked at Unilever I spent several (very enjoyable) years studying the colloid science of toothpaste :-)
While no-one in Britain starves or dies because they cannot afford healthcare there are a lot of Brits for whom life is ... well ... a bit shit right now.
And that's a constituency who are easy to inflame with bogus claims of where the blame lies.
Some are evident typos. Any knowledgeable one can catch those. Others seemed to be out of confusion of the author who apparently took few arguments from one of his books, confused notations and messed the proof.
@naturallyInconsistent the arrangement between the author and publisher is confusing to me, now. If he is not active anymore, who is going to handle further queries regarding the book? Springer authority was kind of indifferent in their response.
I wish my guy was middle aged one (that is what I imagined for no reason). But lately I saw he is out of academia for quite some times. And now does religious preaching.
@Allie I think it is dangerous to throw out the baby with the bathwater: Just because there is a lot of bad and/or useless philosophy doesn't mean there isn't valuable philosophy, too. Science does not exist without philosophical preconceptions about the nature of reality and notions of truth and falsity; we've had rather fruitful conversations about the nature of scientific "proof" in the past e.g. here.
But like most subjects it's not something you can just discuss without foundation and expect it to be fruitful, most of philosophy is a response to something that came before rather than some opinion that formed in a vacuum, just like modern physics did not appear out of nothing, and just like it's not very useful today to just give one's opinion on Newtonian mechanics without actually having learned both it and its modern successors
(to most people it would be obvious it's not even really possible to form such an opinion without having learned about the topic), it's also not very useful to just randomly try to generate opinions on philosophical questions without engaging with their history.
It's also important to recognize - precisely in a historical approach to the subject - that philosophy and physics did not use to be seperate, natural science and philosophy used to be done by the same people and understood to just be different variations in the pursuit of "knowledge", i.e. science
(I'm not only responding to you specifically but to the more general resentment of philosophy I read above, though I will not disagree with John in that I also find amateur philosophy tiresome :P)
@Slereah no, Zizek sniffs, throws some insults in your general direction then proceeds to tell a rambling and only tangentially connected anecdote :P
@ACuriousMind got any book recommendation for how we got here culturally? Like from one worldview to another historically? I'd like to read such a book
i have great news i passed my paper discussion retake. tho now im not sure i will work in that lab but at least now i get to choose
also @qwerty i spoke to other students as you suggested. i found out a scary piece of data. in the time the grad student i spoke to had been in the lab he knew 4 PhD students who left. 2 of them left physics entirely. xD i started discussing with another group that had no "process" other than a brief chat w the professor, and he welcomed me to the lab meetings. im getting much better vibes from the second prof, but still keeping my options open
When I considered the i.e Moeller scattering, in order to construct the feynman diagrams I used wick contraction to do so.
If I am asked for a process, i.e electron positron scattering to muon pair, to draw the corresponding feynman diagrams and write down the associated matrix element.
How could I do such a thing without having knowledge of the interaction term of the lagrangian density
Presumably either a previous exercise or the lecture discussed the part of the Standard Model Lagrangian relevant for this. If an exercise does not specify, you are usually meant to compute the real-world value, i.e. what the Standard Model says
@ACuriousMind I derived the feynman diagrams for moller scattering from the given interaction term and the wick contractions. That was, perhaps long but extremely easy to do
@imbAF ...you mean to tell me you did the derivation of the diagrams for one specific case without deriving a general procedure for how to draw and compute diagrams for general interactions?
@ACuriousMind Mhhh, you have the QED lagrangian without flavor changing terms $\sum_i \overbar{\psi}_i\gamma^\muA_\mu\psi_i$. I'm pretty sure there is this example in P&S chapt 5
@ACuriousMind I am not saying that, obviously . All I am saying sketching the diagrams from the contractions between ladder operators and field operators was super easy
Is it weird to say that the propagator, came to be (its nature) only after contractions were made, for the moller scattering, it was between massless vector field, and thus you have virtual photons. But this all took place with the interaction term given
I fail to see how the rules given say anything about the propagator, whether its because of virtual photons or virtual electrons or virtual other fermion particles
In the compton scattering, I thought of how the interaction term would look like, and after doing contractions for 2nd order, I found out that the propagator was the result of the contraction between two spin 1/2 field operators
you do the derivation Lagrangian -> LSZ formula -> Wick's theorem -> Feynman diagrams once, and after that you compute scattering amplitudes just by the Feynman rules that tell you which diagrams to draw
to every interaction term there belongs a kind of allowed vertex
and then you just draw all the diagrams that are possible to construct from those vertices up to the desired order
no one does those contractions etc. explicitly anymore, that's the whole point of the nice diagrammatic language - you don't need to really think about anything except drawing the diagrams right
@ACuriousMind For some reason it's taking very long to upload the pic, it's quite a standard usage. Some call it Standard Model QED. Incidentally, I don't take the "electro" in QED as "electron", rather as "electromagnetism", so I'm fine with leptons in the club :P
If you really understand how the diagrams work, someone can give you a Lagrangian and you can just go directly to drawing the diagrams and computing them, no steps in between necessary
Presumably either a previous exercise or the lecture discussed the part of the Standard Model Lagrangian relevant for this. If an exercise does not specify, you are usually meant to compute the real-world value, i.e. what the Standard Model says
You have simply overlooked some contextual clue that would have told you the Lagrangian; without knowing your exercise and lecture in detail, I cannot tell you which (and I'm not really interested in finding out), unless whoever wrote this exercise messed up (and then they should immediately correct it if you ask them).
your description is extremely strange - one the one hand you talk about deriving the diagram values from Wick contractions etc., then you talk about "receiving" Feynman rules as if they just dropped from the sky without derivation
It's best just to ignore the Feynman rules for now and just expand the correlators to first order and do that first. And then maybe work backwards to see why you can just use the Feynman rules from the beginning
@HerrFeinmann seems helpful, feels like cheating if it is assumed that I should know how to solve it with the info I am given. But might peep at this eventually xD
@ACuriousMind They did. They were given to use from the lecturer just like that. "A recipe" in QED
That is all I can say
And tbh I find this
@ACuriousMind so much simpler lol
And ACD in what I uploaded in the end, if you read the first line it says: "From the considerations in 7. we can derive the following Feynman rules:", 7. was the Moellec scattering example/consideration
@ACuriousMind I compute diagrams from knowing the interction term and the wick contractions. I can then easily interpret the wick contractions among field operators and ladder operators and among themselves, and I can get the feynman diagrams. Then I consider all the relevant wick contraction variations and translate them to feynman diagrams
It is very easy, extremely easy
Maybe taxing in calculating the Wick terms, but that is it really
oh and one more thing @Relativisticcucumber the size and structure of labs matter. I don't know about experimentalist groups but I can speak about groups more on theory side: more than 2-3 PhD students at a time is also a red flag. I was at a group with 10 -11 at one point, NO postdocs and a french colleague was in literal shock because he told me there is no way we were getting adequate supervision
I think the PI was skirting rules the uni had in place for that sort of thing tbh...
(by structure I mean if they PI is hiring loads of PhD students and no postdocs it's not a good sign)
@qwerty oh no this PI has 6 grad students and 1 postdoc. And might take on me and one other grad student (if we both accept/if the other student also passes the interview). Wdyt about this 0.0
@Relativisticcucumber so that makes 7-8 in total? unless there's a few about to graduate that's not so good imo. it's won't hurt to would talk to the past students who left the lab. ask if they feel comfortable having a quick chat with you (zoom call/ email idk - whatever medium feels appropriate - as long as they feel like it's confidential) and see what they have to say about why they left, anything else they have to say
@Relativisticcucumber although the US system is different in that you're spending most of your time in coursework in the first two years right? maybe it could be acceptable in that case... I'm not sure.
