Would it be incorrect to conceptualize a n particle state of different types of particles $|n_1,n_2,....n_N\rangle$ of some arbitrary system as excitations of different types of fields in some region of spacetime where $x_1^0=x_2^0=...x_N^0$ ?
in my cm lectures, we show that if we have free electron plane waves and look at energies from the hartree fock equations, we get a sizeable correction to naive free electron energies. then we go into a lecture on screening to explain why the correction might not actually be so sizeable. the problem is, to me screening only makes sense to wash out fields of different charges. e.g. electrons can shield attraction to the nucleus. how can electrons screen out other electrons tho?
@Relativisticcucumber I recently wrote somewhere about this issue. Maybe trying to call it screening is just wrong. Instead, the exchange interaction comes from Coulomb interaction and is way too strong when implemented as a Slater determinant. A Slater determinant, by being a determinant, guarantees that the probability density of an electron to be somewhere, is independent of all the other electron's positions. But this is nonsense: if an electron is known to be somewhere, then Coulomb potential would
push other electrons far away from that point, resulting in a Coulomb hole in configuration space. That is why it is called correlation, and is not at all captured by a Slater determinant, by definition of correlation under Hartree-Fock. This means that the exchange interaction as computed from a Slater determinant is guaranteed to be an overestimate of the actual residual Coulomb interaction coming from fermion statistics. This way, I avoided the use of screening to explain this important fact.
@SillyGoose miao miao gave some...
@SillyGoose shortcomings? You aren't likely to get it in a textbook... Alternatives and various forms? Ah, I see you are looking for MTW lol
@SillyGoose That's because when you are good at tensor indices manipulations, the whole requirement to deal with transposes disappear. The index notation sweeps away all these unnecessary noise when trying to get to correct equations, and only when you are required to implement the tensor equations as matrices, do you actually need to figure out the transposing. A notation that eliminates noise and clutter is appreciated.
@SillyGoose This is because physics textbook authors are 1) lazy, 2) under immense time constraints to teach horribly complicated physics and don't have time to cover, at time of instruction, mathematical details irrelevant to the difficult physics being taught. Of course the details matter, but you cannot see the details from Cartesian coördinates in Euclidean or Minkowski metric. You will at least require curvilinear coördinates in order to realise that the difference matters. Now, after
generations of physicists doing these "blind leading the blind" kind of dance, it is no wonder that even lecturers themselves, who may have absolutely no difficulty solving problems and getting correct answers, are confused about which entities are a (1,1) tensors and which are (0,2) tensors.
@Relativisticcucumber This is not what miao miao meant, since miao miao had expressedly avoided using screening as the actual physical mechanism to discuss the matter, but yes, in a condensed matter system, it will also be necessary to discuss screening. You can learn about screening quite understandably in plasma physics, where they discuss what happens if you have ionised plasma and you introduce a charge into the plasma. The physical situation is cleaner and clearer there, and then we reuse the concept
@SillyGoose Your suggestion is bad! At least by using the correct word "tensor", an unsuspecting mathematician might be able to search for the correct term in the mathematical literature and decipher what the physicist is saying. Those stuff are not mere matrices; they obey the correct tensor transformation laws, which matrices are not required to obey.
@naturallyInconsistent hm i will take a look at MTW during the coming break
@naturallyInconsistent but that is not the mathematician's definition of tensor
Separately, going back to Leinaas & Myrheim, so is part of the idea that a quantum state can be thought of as a classical field $\Phi: X \to V$ that transforms under a choice of a (restricted subset of) irreducible representation $\pi: \pi_1(X) \to U(V)$?
Classical field since the field is not operator-valued.
I was trying to think concretely. Consider the vector bundle $(X, \mathbb{C}^2 \otimes \mathbb{C}^2, E, \pi)$ where $\pi$ here is the projection as describing two identical particles. Then we describe quantum states as sections of this vector bundle. A simple example might be $\Psi(x) := \alpha(x) \psi_1 \otimes \psi_2$.
Then, we define interchanging the two particles by acting with a non-trivial element of the image of a non-trivial unitary irrep, let's call the element $P_{[\gamma]}$, in the same way that we do in usual field theory: pointwise. I.e., $\Psi(x) \mapsto \alpha(x) P_{[\gamma]} \psi_1 \otimes \psi_2$.
Is this a fair assessment of what is being done in Leinaas & myrheim?
@SillyGoose so what? The physicist would care that it takes on the transformation properties; the mathematician would define something else, but it would still map cleanly onto the same entity. The two sides would not choose for totally incompatible things to be called the same thing.
at least, we are not at that level of antagonistic relationship
@TobiasFünke South Korea just had declared an emergency martial law that the president could only push through for 6 hours and then got struck down as unnecessary by the parliament. Yet, the deposal of the president also took quite a lot of effort, and it was only after many days that it finally got through. It is not just Europe that is going through hard times.
Is there constructed some set of physical laws from which we can logically obtain that any function that can be implemented in some device is Turing computable?
EDIT
I believe that if we restrict ourselves to classical mechanics (I mean if we suppose that any device obey just classical mechanic...
@bolbteppa I feel a bit sad about this and other things sabine puts out these days. i used to be a casual reader of sabine's blog 10 years ago and now it feels like all she does is just clickbait/ragebait videos.
@qwerty I agree, but it's making her a lot of money. If I was offered the chance of compromising my principles for a million subscriber YouTube channel I would be sorely tempted.
@JohnRennie I don't even think she thinks she's compromising her principles. she has beef with academia (and fair enough) and I think she thinks she's taking it to "its logical conclusions", if that makes sense.
@qwerty I suspect it's a gradual transition. Even after she was forced to quit academia her blog and channel remained fairly optimistic at first, but it's gradually veered down an overtly anti-establishment path.
her original contrarianism was over things like funding particle accelerators like the LHC. i think that's a defensible view that can be carefully debated, and I seem to recall there was at least attempts to do so on her blog.
it seems to have now spun something broader like "what kind of and quality of academic research should be taxpayer funded?" which is what the linked video was "really" about if you remove the appeal-to-emotion she weaves through it
> "Deep" refers to the high energy of the lepton, which gives it a very short wavelength and hence the ability to probe distances that are small compared with the size of the target hadron, so it can probe "deep inside" the hadron
Well, remember that while elastic scattering conserves energy, inelastic is a spectrum. It goes from no dissipation to total dissipation. That's why you have "deep"
In this context it happens by interacting with the internal structure of non-elementary particles such as hadrons
And since we don't really know that structure (which would entail deriving hadrons from elementary QCD, a big deal), we have to make guesses with these structure functions that are born combining basic hypothesis+phenomenological input
@ACuriousMind Yes, I think I now fully understand! The slicing into $V_t$ induces a slicing of $M$ into $M_t$, after choosing an origin (at least then I am able to explicitly construct these). And the origin just leads to a shift in the time-label of these spaces. Thank you again.
@TobiasFünke I had a bad feeling regarding cm initially due to material science and chemistry, but I feel many-body theory is quite theoretical and (possibly)rigorous?
@Arjun well, condensed matter is a huuuuge field, so it really depends what exactly you mean
yes, many-body theory can be very theoretical, in fact it uses the same/very similar techniques the high energy people use (feynman diagrams and so on). There are also a few people I know of which are really rigorous (in a math sense), so yes, that is possible (at least to a certain extent) too
@TobiasFünke I've heard some areas in cm use qft(I guess many-body theory does),but am not quite sure which and how it's used,would love to hear from you : )
Every time I read about quantum field theories, I wrongly assume and associate the theory to the Standard Model, that is, our current theory of particles and interactions.
However, it seems that the Standard Model is just a type of Quantum Field Theory, of many existent. Unfortunately, everywhere...
well, which semester are you? have you studied Green's functions in the context of many-body theory/relativistic QFT already at some point?
long story short: yes, QFT (and its techniques: second quantization, Green's function, perturbation theory etc.) are used in condensed matter. In particular, when you want to describe many-body systems and study its excitations, quasi particles and so on. It is a huge topic in itself, with many different applications...
but high energy physics too, no? scattering amplitudes etc.
it is the same thing, roughly. In condensed matter you might ask: If I shot an electron with some momentum into a solid, and some electron comes out with a certain different momentum, what happens? How is the solid excited? etc. And this leads you to scattering cross-sections too, and to the notion of band structure and so on
very real life indeed
sorry, in my band structure example above it should read: shoot a photon, and an electron comes out (that's ARPES simplified lol)
:) so I guess it is worth to try out and visit some courses if possible. then you'll see if you really like it
but again: Condensed matter is an enormous field, also on the theoretical side, and there are plenty of very interesting research areas and problems to encounter
btw: there is a classic paper: "More is different" by Anderson, which might be of interest.
@TobiasFünke I'm planning on to build my QM knowledge now after that maybe learn some qft and then many body physics or maybe you think I should jump into many-body physics right after qm and do qft on the side?
@Arjun it depends on what you mean with "many-body" and "qft" exactly. some people use that more or less interchangeably. Many-body can for example just mean "treatment of many-particle systems in QM", e.g. second quantization....
@SillyGoose I wouldn't call that a "classical field" - it's just the wavefunction - but otherwise yes.
@SillyGoose I don't really follow your notation here - what is $\psi_1\otimes \psi_2$ supposed to be? The crux is that the vector bundle might not be trivial when the fundamental group is not trivial, so you can't write a global section as easily like that.
And additionally, would it be accurate to say that the order of perturbation is a deciding factor in whether all the particles at hand, incoming and outgoing, fully or partially interact?
@TobiasFünke that's so huge, that you could be one of the many rockstars making the tools we all pray to...
@Arjun there are plenty of people, both physicists and chemists, who do many-body physics only within the independent particle approximation, maybe with a bit of renormalisation. That means that they can just do everything within basic QM mathematics, nothing QFT, except for a bit of toddler renormalisation.
@TobiasFünke the research project ended; my wonderful advisor decided to try the commercial world (and get permanent residence, and finally some spare cash), and so miao miao jumped ship to quantum computing. When miao miao described what miao miao was doing in QC to my current colleagues, quite a few of whom also came from QC, they said miao miao dodged a bullet in QC. They also have their own QC horror stories. Anyway, it is rare to find a nookooliar fooshun job, so it is worth spending some time
@Arjun theorist by training, but if an experiment needs extra hands, miao miao can do it. Miao miao is the rare kind that shut the experiment sour grapes up in the lab, because miao miao aced both. Not the brightest at everything, but will get things done to a level that people take note.
@TobiasFünke It was only when miao miao left DFT that miao miao realised why the Wannierisation kept failing. For the most stupid rookie mistake: insufficient pseudopotential wavefunctions. But at least miao miao could point out that even advisor didn't know, and the person who was supposed to teach meow meow about Wannierisation, also abruptly left academia before having enough time to warn meow meow about pitfalls like that.
@ACuriousMind I mean to write it down $\pi \circ \Psi$ locally where $\pi$ is the local cartesian product projection and $\Psi$ is some section of the bundle
blebolus it is hard to choose a research direction, even broadly :P
@Arjun saying 'pls dont take offense' doesnt make what you say inoffensive, it just shows that u r aware of ur potential to offend, which is somehow worse.
@HerrFeinmann this relates to a super weird trend in the states that ive noticed. ppl will ask me like where r u from and i say im american and they are like no where are you really from and im always like ??? i just told you im from here. some people in the states seem to have a fetish for insisting that you cannot describe your heritage as american. outside the US, i have never experienced this sort of thing.
also what makes it esp. weird is theres nothing ab me to indicate that i even might be from somewhere else
i know you will read this and be like "ur chinese what r u talking ab" @HerrFeinmann
i guess the conclusion is that despite all evidence pointing to the contrary people refuse to believe i am not chinese xD the funny thing is ive even been to meet family members of asian people i know and they say "you look alike" when i literally look the OPPOSITE @HerrFeinmann what is it about me pls help me understand xD
@Relativisticcucumber Some people get hung up on the weirdest things. I have an Indian colleague who kept asking me where I'm from and he really didn't want to accept "Germany" (or any of the specifics I gave him) as an answer because I "didn't sound like a German" to him :P
@ACuriousMind Well I've had a fellow Indian ask me which part of the country I was from,when I said I'm from the south he was like no you don't look like that at all lol,then he asked me where my parents are from,I said they are from the same region and then he even asked me about my grandparents lol
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@Relativisticcucumber imo "where are you from" and "what is your heritage" are different questions. I think a lot of the time people just dont have the vocab to ask you what they might actually mean. or they're conflating different things, like physicists talking to mathematicians lol
@SillyGoose I mean - it's not a classical field, it's a wavefunction. That's not a statement about its mathematical nature but about its physical meaning.
@Allie I imagine $h\nu$ can be described as the characteristic energy gap between two adjacent energy levels in the system. For a harmonic oscillator, the energy gap is literally always $h\nu$.
I would have to look back at some notes, but I imagine classically you can approximate an atomic bond between two atoms as two masses connected by a spring, which can then be treated as a harmonic oscillator. Then, quantum mechanically you just treat it like a quantum harmonic oscillator. But I don't recall if there is just one "fundamental" frequency associated with a given atomic bond (in the simple classical model).
I have never had this issue when using Chrome, but I recently switched to Safari and noticed this to be the case. The problem is independent of the document, but the lag seems to go away if I zoom far enough out of the document.
But I don't think I've ever been there - the Philosophenweg is a similarly rich neighbourhood but there's also some physics institutes there so I'm more familiar with it
@qwerty "AI" isn't for people who have their own thoughts or style :P
@ACuriousMind I hate how in many products they make it very difficult to find the settings to turn it off. in the most recent android update on my phone, it turned on some new "smart reply" function that was absolutely infuriating and the off toggle was buried 3layers deep in the obscure unsearchable settings
as searching "smart reply" gave you two other smart reply settings but not the actual setting for the update
@qwerty That's because they need you to use it so they can justify the investment to their bosses ("look how many users are using our new feature!")! They know it's garbage.
or, conversely, they only built it because the bosses wanted it and if the bosses don't see the feature being used they'll just blame the people who built it instead of admitting they don't understand what they're doing