The h Bar

Silly Goose

00:35

@qwerty what type of tea do you like

qwerty

00:58

@SillyGoose I love all kinds of tea but I do not have a sophisticated palate.

Relativisticcucumber

@qwerty even kombucha ?

so tmu, bloch states are delocalized -- does this not imply that electrons in a solid are delocalized? if so, what should i make of this? it seems a bit strange

qwerty

@Relativisticcucumber haha not a big fan of kombucha but I drink it if offered

Relativisticcucumber

@qwerty i will not. i cant do the smell

i am currently drinking an earl grey tea

it is good

qwerty

01:19

earl grey... is so grey. :p I like my milk teas robust and richly coloured. do you have a favourite?

naturallyInconsistent

01:43

@Relativisticcucumber of course it is delocalised, just like how molecular orbitals are delocalised from one atom and is actually an orbital of the entire molecule at once

naturallyInconsistent

01:57

@SillyGoose Lorentz factor, i.e. $\gamma$ and its powers, including reciprocal powers, are dimensionless. You certainly know this, so why are you asking this at all? There is no possibility for dimensional analysis to help you figure out which power of it goes where.

@Relativisticcucumber Self-contained is nice, but the clincher is that it is nice to read!

@Mr.Feynman I'm not sure why you are trying to teach QFT to a person who hasnt seen enough of basic QM. Surely that is even less efficient than confusing notes?

Silly Goose

02:53

@naturallyInconsistent well i was just thinking as a heuristic, not a systematic/rigorous approach

If I have two straight infinite wires carrying current $I_1$ and $I_2$, the force that $I_2$ exerts on $I_1$ is infinite, right?

Concretely, $\lvert F \lvert \propto L$ where $L$ is the length of the wire, which is infinite.

Relativisticcucumber

03:32

@naturallyInconsistent but isnt this delocalization much more substantial? its like delocalized across the entire lattice??

@qwerty ooh milk tea. hm. so when i have milk tea its usually boba, otherwise im a water base person. for milk tea i like any black tea base, but for drinking tea i like earl grey, english breakfast, or cinnamon black tea. i am not super into tea, more of a coffee person.

qwerty

03:57

:) am I correct in surmising that silly goose and and relativistic cucumber are a finite simple group of order 2?

naturallyInconsistent

04:27

@SillyGoose It wont even work as a heuristic...

@Relativisticcucumber why is that surprising? It should be delocalised over the entire lattice. All of them should be!

@SillyGoose correct

naturallyInconsistent

05:16

@qwerty that's a nice song video

qwerty

why not 3?~

I find these things a bit cringe on the whole, but yes :p

naturallyInconsistent

05:46

@qwerty smirks

what makes you think it ain't already manifold?

qwerty

@naturallyInconsistent oh in your case I'm utterly unsurprised

naturallyInconsistent

miehehehehe

Ryder Rude

06:46

hi

think_meaning_buildß

hi

ACuriousMind

Oct 29, 2022 at 19:53, by ACuriousMind

there's nothing in the rules forbidding relationships between geese and cucumbers

think_meaning_buildß

>_>

<_<

naturallyInconsistent

lol

Ryder Rude

07:17

are u Frequentist or Bayesian

Mr. Feynman

@naturallyInconsistent I don't know well the background of users here, except ACM, you, the wacky fowl, the lorentzian vegetable and few others

You sure have many "enemies" in the chat :P

qwerty

@Mr.Feynman the cat haz claws. one must be careful to not brush fur the wrong way :P

Ryder Rude

Probability interpretations

The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory. There are two broad categories of probability interpretations which can be called "physical" and "evidential" probabilities. Physical probabilities, which are also called objective or frequency...

Mr. Feynman

Which reminds me that I have to try something today

I have read that if you brush your cat's head with a wet toothbrush, it feels like its mother licking its head

So I will indulge in such activity after waking up. Now it is indeed time to go to bed and get some more rest~

qwerty

i thought it was morning in europe

sweet dreams

ACuriousMind

07:25

It is

I'm on my way to work :P

qwerty

I should try and fix my sleep cycle so I can do some physics before I work. I'm too tired when I get home

do any of you edit physics on wikipedia?

there's some self-researched physics article on there that's hung around for dogs' years but I don't know wikipedian culture enough to either handle it myself or push for someone else to deal with it.

naturallyInconsistent

@Mr.Feynman well, one thing you can do, is that before you answer someone, search the chat log for their prior engagements. If you see ACM scolding someone for certain reasons, you will know whether to expend the effort or not.

@qwerty sharpens with nail file

good night

@qwerty do it~ Good intro to editing wiki

qwerty

07:44

@naturallyInconsistent It's a big endeavour. I've only ever done minor edits. I don't really know if I can/should just... delete it, ask someone else to delete it, bother editing it, merge it or whatever.

Actually I tried to ask about it on the main phys.SE site yoinks ago (before I discovered chat and realised the main site isn't really for that kind of question) and you commented saying "yeah it's wrong" lol

nickbros123

07:57

@RyderRude I'm more of a "guess the probability distribution based on vibes" kinda guy

Ryder Rude

@nickbros123 that is sort-of Bayesian. But the key question is, what does probability distribution mean to u

nickbros123

it means a lot to me

its like a friend

Ryder Rude

then u hold it dear

Mr. Feynman

@naturallyInconsistent I think everyone trying to learn is worth the effort

4

I have been - and often am - on the other side and getting a reply is soothing. Living in a world with no replies is sad and haunting

qwerty

@Mr.Feynman indeed, kindness is everything.

2

and we shouldn't be quick to judge.

Slereah

08:10

@ACuriousMind what is the proper way to deal with propagators as distributions instead of doing weird contour rules or putting in infinitesimal parts

From the contour I'm guessing homotopy is involved

qwerty

@Mr.Feynman I was openly told by some lecturers how they tierzooed their students (as fish - a reference to the red dwarf skit "you wrote in your exam 'I am a fish'", rabbits or otters). it's just sad.

Mr. Feynman

@qwerty I'm not kind, I'm a self-projecting, self-centered disagreeable snake :P

qwerty

why is hbar such a menagerie lol

Mr. Feynman

@qwerty Hmmm this is not bad to me, if you keep it to yourself and do not make distinctions

Slereah

@qwerty How did you rank

qwerty

08:12

@Slereah LOL. I was told I was a run-of-the-mill bunny

Mr. Feynman

@qwerty "snake" as as "unpleasant". It's already established that I'm a human. A stereotypical pizzaiolo

qwerty

@Mr.Feynman it made its way to me as a 3rd-year student, and it was amongst more 2 lecturers... so it was not kept to oneself...

Mr. Feynman

@qwerty No yeah, what I meant is that as long as you don't make it public and humiliate students, it's okay. It's something that happens in every aspect of life, not just physics

As long as you don't make a poor student feel uncomfortable or not good enough I think it's fine

qwerty

@Mr.Feynman well, I will say that some people are certainly more judgemental than others, and take pride in it. if you are accepted in their inner circle/clique, it makes you feel special and more talented in turn.

of course we all have judgements to some degree, but I definitely believe that there are unhealthy amounts to which people do it

Mr. Feynman

After all physicists are humans and flawed and so they are subject to the same unpleasant social behaviours as other human beings in other fields. It may be surprising and disappoint because of how much content-centered (and not person-centered) science is supposed to be, but that's utopia after all

So I don't think it is about physics. Well, this is what I've come to think over the years. In the past I would be more concerned about certain issues, expecting physicsts to be the pinnacle of our kind, flawless beings resonating with the sacred study of the wordly laws.

Then I learned about EFT

qwerty

08:23

yes, but we should try to be conscious of these things, and reject it when we can. it's like learning the world is unfair: we know we can't make the world fair, but it doesnt give us an excuse to act like arseholes

Mr. Feynman

Yes, that's true and probably someone acting like an ass wouldn't agree with me in the first place. Even then, the whole concept of acting like an ass is about how your actions affect others. I think a lot of things are alright as long as they do not affect others

Slereah

People sometimes wonder what is the source of the greek miracle in intellectual life

I have found the source

> Demetrius of Phalerum, as keeper of the king's library, received large grants of public money with a view to his collecting, if possible, all the books in the world

Large grants

plz give physicists large grants

Mr. Feynman

Shut up you are getting no money

But you may have some ice cream

qwerty

@Slereah aren't you out of academia?

Mr. Feynman

Okay, I probably look mentally unhinged on this chat, but I swear I'm normal

Slereah

08:29

@qwerty Yes, exactly because of that

qwerty

@Mr.Feynman I don't think there's a single normie in this chat.

Mr. Feynman

So your deadly sin is Greed

@qwerty normal, not normie. We're no normies :P

qwerty

normie, normal. what's the difference?

Mr. Feynman

Mhhhh, because with "normal" I meant that I'm not unhinged :P

While normie is typically the opposite of geek/nerd

qwerty

I'm afraid you're neither, mr F

Mr. Feynman

08:34

Mhhh, not a geek. But not a nerd?!

qwerty

oh, I meant neither normie nor normal :)

naturallyInconsistent

@qwerty iirc, didn't miao miao edit it when discovered?

Mr. Feynman

@qwerty Lmao

qwerty

@naturallyInconsistent I don't think so? It was a full article full of one guy's own computations

naturallyInconsistent

@qwerty There is "shouldn't be quick to judge", and then there is 123, my dear

@qwerty oh, yeah, then that ought to be deleted

miao miao was referring to the earlier case when you posted to the main site

qwerty

08:38

I last checked it maybe a month ago and I was disappointed the article with the banner I put on it was still there, and iirc there was a second article with a section from the same guy

naturallyInconsistent

name and shame

@Mr.Feynman have you not seen that miao miao had been going through the chat logs basically daily and answering to basically everything?

qwerty

@naturallyInconsistent here's the question on the main site from before I realised it was possibly bad form physics.stackexchange.com/questions/810817/…

naturallyInconsistent

@Mr.Feynman Japan showed the world what happens when people really really want to learn, and from then on, the powers that be are all reticient in teaching.

qwerty

@naturallyInconsistent if I were to untangle it then it would probably be substantial work, and I'm not confident to not... introduce new errors.

naturallyInconsistent

yeah, that seems to be a big undertaking. I'm also reticient

qwerty

08:52

I think from the history/talk page it was a spillover from an edit war from many years ago as well

wiki culture makes me nervous lol

Mr. Feynman

@naturallyInconsistent yes. I'm the opposite in that regard. Too lazy :P

@naturallyInconsistent I think I don't understand what you are talking about here

qwerty

@Mr.Feynman seconded

naturallyInconsistent

@Mr.Feynman Japan was very much technologically backwards before the Americans bashed open a port. And then suddenly they were a power strong enough to defeat colonial powers in WWII.

@qwerty yeah, same

naturallyInconsistent

09:13

@qwerty do tell meow meow which ones to pay attention to. Miao miao just added a proposal for deletion on that offending page. Reading Brews Ohare's own little section on wikipedia is kinda unhinged

qwerty

@naturallyInconsistent I believe it's all documented in the question I put the main site; mostly the first two links to wiki.

@naturallyInconsistent yis brew ohare was a bit... typical of the retired engineer does physics stereotype

naturallyInconsistent

lol

Tobias Fünke

good morning

@qwerty can you provide examples? I think some WIkipedia articles are really good, some are meh, but not too false

qwerty

@TobiasFünke continue reading the convo - it was about a specific one

Tobias Fünke

@qwerty sorry, okay.

@Slereah may I "advertise" my answer here: Is that what you are looking for?

4

Q: Why do different contours give different answers in the limit $\epsilon \rightarrow 0$ when calculating propagators?

Let $\phi$ denote the Klein-Gordon field. Then its propagator $\langle 0 \mid [\phi(x), \phi(y)] \mid 0 \rangle$ can be calculated as $$\int \frac{d^4}{(2\pi)^3} \frac{-e^{-ip(x-y)}}{p^2 -m ^2}. \tag{1}$$ Isolating just the $p^0$ part of this integral, which is where the problem is, we get $$\int...

Indeed, you should view propagators as distributions

naturallyInconsistent

09:27

@qwerty 2nd link was also crazy; the statement just previous to that offending section literally stated that there is no appearance of fictitious forces just because one changes from Cartesian to polar. Miao miao have removed that section.

qwerty

@naturallyInconsistent thanks so much. I wanted to go in and delete things but do not have the wiki boldness

couldn't believe how many years it lingered on there being blatantly incorrect

naturallyInconsistent

If you see more, tell us.

Slereah

@TobiasFünke doesn't really contain what I want !

Tobias Fünke

okay, then nvm

qwerty

@naturallyInconsistent sure. i notice you don't have a wikipedia account?

naturallyInconsistent

09:38

@qwerty actually I do, but after moving around from place to place and changing computers, it is annoying to have to login

@TobiasFünke it was good nonetheless~

Tobias Fünke

@naturallyInconsistent thanks <3

@naturallyInconsistent May I ask: You live in the US, no?

naturallyInconsistent

@TobiasFünke nopeu~

NOTE Book

10:13

Hi

Tobias Fünke

hey

NOTE Book

can you pls tell under what conditions does like charges attract? More specifically shall size of one object be smaller?

@SillyGoose that is a penguin

Tobias Fünke

Do you know Coulomb's law? What can you conclude from that?

NOTE Book

yes it gives relation between forces of charges at rest

i know there should be large difference in magnitude of charges and that they should be placed closed to each other

but does size of objects also help in induction?

Dannyu NDos

1. The difference of magnitude of charges don't matter. The more they are, they stronger they attract/repel. 2. The actual size of objects don't matter either. 3. Provided that the objects involved both have nonzero charges, they always attract/repel.

Their signatures decide whether it's an attract or a repel.

NOTE Book

10:21

but if both the bodies have equal charges how will they induce and attract

uh..i actually meant Net attraction

Dannyu NDos

Some misconceptions seem to be going on here...

NOTE Book

wait i will ask more clearly

Under what conditions can like charged bodies attract each other more than they repel?

naturallyInconsistent

There are many cases that such a thing can happen

you need to have an idea what it is you want to actually ask

NOTE Book

the favourable conditions

Tobias Fünke

Perhaps it is worth to think about what exactly you want to ask, and to formulate a separate question on the main site (?). Depending on the question you ask, the answer can be far from trivial, I am afraid.

Dannyu NDos

10:27

Are you asking about like, charged conductors, rather than individual charges?

NOTE Book

Yes like charged conductor or extended bodies

Dannyu NDos

It might be good to look at electrostatic induction and Van der Waals force.

naturallyInconsistent

@TobiasFünke It can also be really trivial. Even the most basic case: conducting sphere already can have like charges attract.

Tobias Fünke

yeah

naturallyInconsistent

It feels like an attempt at premature generalisation

Silly Goose

14:14

Here, $P_\text{field}$ is the volume integral of the Poynting vector and $\frac{d}{dt} P_\text{mech}$ is the total electromagnetic force exerted on currents/charge in the same volume.

Why is the poynting vector associated with the electromagnetic momentum? Shouldn't the stress tensor (by conservation law definition of momentum) contain all of the field's momentum?

In this frankenstein of particle and field theory, it is conceivable that the total momentum should be $\text{net particle momentum} + \text{net field momentum}$. I probably am misunderstanding, but I don't see how this could be consistent with 6.122.

Silly Goose

14:34

Oh I think i am being islly

Mr. Feynman

@SillyGoose Mind that despite the unfortunate notation, that is the spatial energy-momentum tensor

In other words the indices are $(1,2,3)$, not $(0,1,2,3)$, like the one you may have seen in relativity

The energy or momentum densities are enclosed in the $T_{0i}$, $i$ spatial index of the energy momentum tensor. That one you have there is just $T_{ij}$

If there are no particles and $P=P_{\text{field}}$, your equation:

$$dP_i/dt=\sum_j\partial_{j}T_{ji}$$ would instead take the form $\partial_{\mu}T^{\mu\nu}=0$ in special relativity

Summation understood over all four indices (the minus sign comes from the metric if you write this down)

($\partial_0 T^{0\nu}+\partial_{i}T^{i\nu}$ and note that the time component is the energy Poynting theorem)

Silly Goose

14:59

Hm I think I see. If we add particles into the system, then do we just add the lorentz force law density to your expression $f_i = \rho E_i + \epsilon_{ijk}j_{j} B_{k}$?

Since this is what we should take as the rate of change of momentum of the particles (due to Newton's second law)

Mr. Feynman

15:12

You have derived this equation starting from Newton's second law (and Lorentz force) for matter (particles). Now, the equation you have derived $(6.122)$ is general and always holds true. I considered the case where $P_{mech}=0$ because there are no particles to make a simple comparison with relativity

imbAF

If I were to consider a system of two electrons, which can be considered as subsystems. Then the Hilbert space of the entire system is a tensor product space or a sum of the Hilbert spaces of the sub systems?

When the basis of the total system is a tensor product basis

What can one say about the Hilbert space of the entire system?

Mr. Feynman

A tensor product, not a direct sum.

Now, @SillyGoose if it troubles you that you started using particles and the result can also be used without particles, just mind that you could use Maxwell equations to derive the field-only case without considering Lorentz force

imbAF

what is the difference?

in construction

Tobias Fünke

@imbAF The Hilbert space of two electrons is the anti-symmetric subspace of the tensor product of the two single-particle Hilbert spaces.

imbAF

why subspace?

Mr. Feynman

15:16

Yes, I was imprecise. You have to antisymmetrize due to indistinguishability

imbAF

Well maybe I need to explain something

Mr. Feynman

@imbAF For the reason I have just stated, indistinguishability imposes the antisymmetry constraint on fermion states

imbAF

I know about the indistingishability

I don't see how it causes

the consideration of a sub space

for the entire system

and not simply the hilbert space of the entire system

Mr. Feynman

antisymmetric tensors form a subspace

imbAF

subspace of?

Mr. Feynman

15:19

You have the tensor product, which is made up of tensor products of states; you are only interested in antisymmetrized ones, which are a subspace thereof

Tobias Fünke

---the tensor product of the single-particle Hilbert space with itself, as I've just said

@imbAF there are important differences between direct sum and tensor product. You should check the definition(s). Also, there are one or two nice questions on the main site concerning this, which I think you are able to find yourself

imbAF

I think I am missing a key element into understanding what is going on. Perhaps I need to clarify, why I even asked that question in the first place

So I need to clarify what my aim is and what I don't fully understand and what I take as granted, which perhaps is wrong to consider

Tobias Fünke

irrespective of your current problem which you are trying to solve, I think it is important to understand this matter at some point of your studies! so don't forget it ;)

imbAF

Of course

Tobias Fünke

That being said, didn't you ask several questions already about Fock spaces and creation- and annihilation operators?

imbAF

15:22

I am writing right now what I want to know and find the issue

In my lecture today we said that the Fock space is a direct sum of Hilbert spaces of N particle states. This sounds not accurate, I would very much say that the Fock space is a direct sum of Hilbert spaces of different number of particles. Saying it as in the first attempt, gives me the wrong impression that we are only considering states which describe N particles, when that is not the case because the Fock state contains the Hilbert spaces of a system of 0 particles, 1, 2....N.
With this being said, I remembered that a Hilbert space of a system can also be considered as a tensor product o…

is basically e.g for a system of two electroos: $|n_1,n_2\rangle= |n_1\rangle (1_1 + 1_2) x|n_1\rangle (1_1 + 1_2$ where $1_i$ is the unity and 1 and 2 indices show the unit matrix in two different hilbert spaces

So this is what I understand with tensor product basis, at least

And apart from, understanding the use of the term "tensor" - product basis/ space

I want to understand the structural difference between a space that is a tensor product space and one that is a direct sum

That means, how do we represent basis elements in both spaces

and how do arbitrary elements look like

when compared to each other

Silly Goose

@Mr.Feynman I was meaning to ask about what needs to be added to the field (no particle) conservation law to get a field+particles conservation law.

Hm wait I think maybe I see where I am getting confused.

The equation 6.122 is derived from considering the rate of change of momentum of particles in a volume. This corresponds more abstractly to considering the energy-momentum tensor of particles only subject to some electromagnetic field. In particular, the starting point of this derivation excludes the energy-momentum tensor of the electromagnetic field itself. Is that correct?

My question then is, why do not consider the full action $S := S_\text{particles} + S_\text{EM} + S_\text{interaction}$ for deriving conservation laws? I mean the total system should be particles and the field, right?

Mr. Feynman

15:41

@SillyGoose If I recall correctly you are familiar with Noether theorem, I think you have discussed it lately while studying QFT, right?

A (imho) neater (neater<-->Noether MUAHAHAHA) way to see these things is by means of lagrangians

Silly Goose

@Mr.Feynman Yes

Mr. Feynman

In natural units, the E.M. field lagrangian (density) is $\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$

Silly Goose

(I see the starting point of Noether's theorem as the action, which is why I referred to the action above)

Mr. Feynman

From this you derive the vacuum Maxwell equation and - using spacetime translation invariance - you derive the energy and the momentum Poynting theorem above, just for the fields

Silly Goose

Yes I am fine with that

Mr. Feynman

15:44

If you add the interaction term $-j^\mu A_\mu$ and do the same things you get the full version

Silly Goose

but don't we also need the lagrangian of the particles themselves?

Mr. Feynman

Yes, of course there is also the free particle term

Silly Goose

is what I was asking above. seemingly, we are considering conservation laws for only part of the entire system

it should be $\mathcal{L}_\text{EM} + \mathcal{L}_\text{particles} + \mathcal{L}_\text{interaction}$. then the Noether current for spacetime translations should yield the energy-momentum tensor that we actually care about.

Mr. Feynman

Here, in both version the energy momentum tensor is that of $\mathcal{L}_{EM}$

Silly Goose

so the particles are being treated as external to the system?

Also, aren't we including the interaction lagrangian as well? But even that is strange. to what system does the energy-momentum tensor of $\mathcal{L}_{EM} + \mathcal{L}_\text{interactions}$ belong to?

naturallyInconsistent

16:00

Because of minimal coupling, the interaction is just replacing the kinetic momentum term in the particle part of the Lagrangian with the canonical momentum term, i.e. converting partial derivatives into covariant derivatives.

Mr. Feynman

16:21

@SillyGoose After all the derivation you have followed already takes the charges into account because you start from their EoM (Lorentz) force and from that consider the change in momentum. From that perspective you may see it like this: you are writing the time variation of the total momentum of your particles and in doing this two mysterious quantities appear, which you call respectively "momentum density" of the field and "energy momentum tensor"

The energy momentum tensor of the field accounts for both the field energy and the interaction energy

So the energy content of the particles is basically only kinetic, which you already consider with the $P_{mech}$ term

imbAF

Can someone explain this part here:
https://en.wikipedia.org/wiki/Variational_method_(quantum_mechanics)#:~:text=If%20we%20were,.

what's it meant with "To vary over all possible states with norm 1" ?

What are we varying?

find the expectation value of H, while considering different states? V

Slereah

My eyes

Mr. Feynman

@Slereah What's that?

Tobias Fünke

@imbAF You start by some single-particle Hilbert space $\mathfrak h$. For $N$ indistinguishable fermions, you proceed by constructing the anti-symmetric subspace of the N-fold tensor product of $\mathfrak h$. We can denote this space by $\wedge^N \mathfrak h$. Then the Fock space is defined by $F(\mathfrak h):=\bigoplus\limits_{N=0}^\infty \wedge^N \mathfrak h$, where $\wedge^0 \mathfrak h:=\mathbb C$ and $\wedge^1 \mathfrak h:=\mathfrak h$.

Slereah

@Mr.Feynman Very bad writing

Tobias Fünke

16:32

@imbAF I've already commented on this in some messages above.

Mr. Feynman

@Slereah The scheme seems interesting though. Can you explain very simply what analogy it is trying to make?

Not the analogy per se, just the kind of analogy

Tobias Fünke

The rest of your message I don't really understand, sorry.

Slereah

arxiv.org/pdf/1112.5525

you're welcome to try to decypher it

Tobias Fünke

@imbAF the relation between tensor product spaces and tensors as multilinear maps is explained somewhere on Wikipedia, IRRC.

@imbAF all vectors with norm 1.

imbAF

@TobiasFünke In what you wrote about the Fock space, where can one see the anti symmetry?

@TobiasFünke I will search for them

Tobias Fünke

16:35

@imbAF ... well, I've explicitly stated that, no? $\wedge^N \mathfrak h$ for $N\geq 2$ means the anti-symmetric subspace of the $N$-fold tensor product $\otimes^N\mathfrak h$.

imbAF

Yeah you did describe it

Tobias Fünke

All of this should be explained in basically any textbook dealing with second quantization. Which book do you follow?

imbAF

But I though one could somehow tell by looking at the expression

but it ain't the case

Tobias Fünke

@imbAF sure it is! I've explicitly introduced the anti-symmetric subspace...

imbAF

@TobiasFünke Keine really. We still haven't been introduced properly to 2nd quantization, And we are using notes take from different books. So no coherent explanation is made

Honestly during my bachelor, the term tensor product basis was thrown in

when we cosidered the basis of the hilbert space of 2 electrons which I suppose

in an extended way can be written as:
$|n_1,n_2\rangle= |n_1\rangle (1_1 + 1_2) x|n_1\rangle (1_1 + 1_2$ where $1_i$ is the unity and 1 and 2 indices show the unit matrix in two different hilbert spaces

Tobias Fünke

16:38

If you'd deal with indistinguishable bosons, you would consider the symmetric subspace $\vee^N \mathfrak h$. For distinguishable particles, you would just use the tensor product $\otimes\limits_{i=1}^N \mathfrak h_i$; the Fock spaces, mutatis mutandis, take the same form

imbAF

it's not being compiled

the formula you wrote

Tobias Fünke

@imbAF I cannot follow. Sorry.

Which one?

imbAF

@TobiasFünke here

$\otimes\limits_{i=1}^N \mathfrak h_i$

Tobias Fünke

ok. but you can imagine what it looks like, no?

imbAF

the fock space for distinguishable particles?

Mr. Feynman

16:41

$$\otimes_{i=1}^N \mathfrak{h}_i$$
ftfy

Tobias Fünke

Sorry. I simply mean something like $\otimes^N \mathfrak h$

Mr. Feynman

Ah

You know what? Probably \limits doesn't work with otimes

And you need the big one

Tobias Fünke

could be, yeah

imbAF

No I had no clue

Mr. Feynman

$\bigotimes\limits_{i=1}^N$

imbAF

16:42

Maybe I should have had at this point

Mr. Feynman

Neither... Mh.

imbAF

But not a clue at all

Tobias Fünke

@imbAF If you want my honest advice: Take a good book, learn everything from the beginning. It is not hard, but of course requires work.

imbAF

Once the stupid semester comes to an end and I finish all the mandatory paperworks

Tobias Fünke

@Mr.Feynman remove the first _ ?

imbAF

16:43

which allow me to enter the exam

I will read the entirety of schwarz

and linear algebra done properly

Mr. Feynman

Oh, typing mistake

Tobias Fünke

Second quantization is, in my experience, best explained in condensed matter books. But OK

Mr. Feynman

So it works with the big otimes

Tobias Fünke

nice

Mr. Feynman

Just a check with the small one again

imbAF

16:44

@TobiasFünke such as?

Mr. Feynman

$\otimes\limits_{i=1}^N$

Scientific method applied successfully

Tobias Fünke

@imbAF I know so many books, but I cannot recommend one right now by heart for this specific topic... sorry. Maybe the others here have a recommendation

Mr. Feynman

@TobiasFünke Except for indices, yes :P

Sometimes they use redundant indices (sometimes they are required)

I would advice to check e.g. Bruus&Flensberg

Tobias Fünke

I mean. A book which I like are the ones by Arai. But that's for mathematicians. Runge & Gross is nice but old (and the english version has some typos).

imbAF

Idk how to upload a pdf

Mr. Feynman

16:47

"Many-body quantum theory in condensed matter..."

imbAF

just for people to see

the 2nd quatization "lecture" I got

Tobias Fünke

@Mr.Feynman yeah, that's a standard reference. should be fine, but I cannot remember their chapter on SQ

imbAF

and then that might answer the question, how on earth I don't know about tensor product and direct sum or w/e

Mr. Feynman

@TobiasFünke It's the very first. Honestly, I don't remember that very well either but I'm sure the level is the right one and it's clear enough. I had to review something about 2nd quantization recently but really it's like the 5th subject in which I have too, so I barely skim :P

Then I spend one day with mild index headache

For example, what gave me some headaches this time was learning that the normalization factor for symmetrized states may differ because sum considered a sum over all permutations (most books), others (Landau) consider a sum over distinct permutations

When I say "distinct" I mean that whenever there is a repetition, they neglect the permutation arising from permuting particles already in the same state

Tobias Fünke

@imbAF Listen: Nothing is wrong about not knowing something. And it is good that you ask.. That's perfectly fine. My "honest advice" was just for you to think about if this is really the most efficient way of learning.

Instead of asking question on very specific topics in the maths appearing in physics (say, tensor products, direct sums etc.), you might consider it much more efficient to first learn the overall concepts (at least on a level you can work with, it must not be the level of a mathematician) and then apply these concepts to the specific problem

You must agree that it does not make really sense to think about Fock spaces, anti-symmetric subspaces of the $N$-fold tensor product etc. if you don't know what a tensor product or a direct sum is.

Or am I completely off??

...and if you don't like your lecture (notes), you really should consider to get a book and work with that. And to find a good book that works for you requires some trial and error, too.

...just my two cents. you do you, in the end

naturallyInconsistent

17:07

@TobiasFünke ACM had already scolded him for this specific problem multiple times.

Tobias Fünke

@Mr.Feynman I think Nolting's many-body book is quite nice, actually! (The Nolting books are standard references in Germany for undergrad (or beginning grad) courses, I'd say) --the first chapter is on second quantization, and I think it is really pretty as an introduction.

@naturallyInconsistent Am I too harsh? I really just wanted to help here :d

naturallyInconsistent

@TobiasFünke you arent anywhere near harsh enough

Mr. Feynman

Considering that I'm at the end of my master's and I just have to get rid of the last physics of matter things, I won't need it much, but I'll check it

@TobiasFünke He's actually backing you up :P

Tobias Fünke

Ok :d

naturallyInconsistent

@Mr.Feynman like with a truck?

Mr. Feynman

17:12

@naturallyInconsistent I'm saying it really in a friendly way: I think you probably being harsher than required in these situations D:

naturallyInconsistent

D:

Tobias Fünke

Now they left. :s I feel bad

Mr. Feynman

Ah don't worry, he does that all the time :P

naturallyInconsistent

@TobiasFünke He is doing this to everybody

Tobias Fünke

xD

ok

Mr. Feynman

17:13

2 days ago, by Mr. Feynman

You alread left me hanging once today :P

Tobias Fünke

I see

naturallyInconsistent

It is the standard "help" and not even a "bye", let alone "thanks"

Tobias Fünke

yeah...

Mr. Feynman

Well, thanks Tobias :)

Tobias Fünke

:D

naturallyInconsistent

17:14

:D

~~

Tobias Fünke

It was a pleasure to give a monologue on Fock spaces :s

naturallyInconsistent

M I A O ~

Tobias Fünke

@naturallyInconsistent What is your field of study/research?

naturallyInconsistent

There was also a Fuchs, you know?

@TobiasFünke nookooliar

Tobias Fünke

whut?

naturallyInconsistent

17:15

nuclear

Tobias Fünke

Ah :D

naturallyInconsistent

but miao miao did DFT before

Tobias Fünke

But also in nuclear physics context or chemistry or so?

naturallyInconsistent

it was fun sitting and listening in on all the graphene woes

completely disconnected field of study

Tobias Fünke

I see

naturallyInconsistent

17:17

But it might become useful; we now want to check out what our magic material is doing, and that might require DFT modelling

Tobias Fünke

:)

Okay, I gotta leave now. See you around

naturallyInconsistent

what about you?

oh, bye~

it will be a good night from meow meow

Tobias Fünke

@naturallyInconsistent sorry, next time!

bye

naturallyInconsistent

@Mr.Feynman great choice

Mr. Feynman

I only have one problem with that book

naturallyInconsistent

17:21

what?

Miao miao left the B&F across the ocean. Brought the F&W here

Mr. Feynman

@naturallyInconsistent Unless I'm having trouble with the notation (because I didn't really invest much in that part as I already knew it), in the introduction to GF there is a brief review about the SE Green function

That time integration in $(8.21)$ shouldn't be there

Oh wait wait wait

No, nothing

I mean, the propagator is such that you only make a space convolution

naturallyInconsistent

Well, it has no place in a condensed matter text, at least

Mr. Feynman

Yes, it was something very minor

naturallyInconsistent

If it were in a HEP text, then it does need the time integration. The propagator should be a surface boundary integral of a spacetime region

Mr. Feynman

That is the SE wavefunction, so no HEP in any case

naturallyInconsistent

17:30

Well, annoyingly, the SR version of Hamiltonian evolution of quantum wavefunctions is still called SE

Mr. Feynman

The correct equation should be $$\Psi(\vec{r},t)=\int d^3\vec{r} 'K(\vec{r}t,\vec{r}'t')\Psi(\vec{r}',t')$$

naturallyInconsistent

yes i know

Mr. Feynman

I know that you know, I'm kind of venting :P

naturallyInconsistent

vent away~

Mr. Feynman

And of course the fact that $$G=\theta(t-t')K$$ doesn't change much as the theta doesn't kill the time integration

Ok, vent over

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