@DIRAC1930 when they are short-lived they show up as resonances, otherwise you do Bethe-Salpeter

but generally if you're really interested in bound states the question is whether you actually should be doing QFT :P

for specific bound states (like some particular atom) relativistic QM is usually the more suitable approach; full QFT is not very good at investigating the interacting space of states, as I've repeatedly pointed out

@SillyGoose The equivalence between these two perspectives is indeed provided by the idea that two operators related by unitary transformation can be viewed as the same operator in two different bases (passive interpretation of the unitary transformation).

But it doesn't follow from this that you should always interpret two operators related by unitary transformation as "the same operator": For instance, the Heisenberg picture has $A(t)$ evolve from $A(0)$ unitarily, if we considered $A(t)$ and $A(0)$ the same what would be the point? Commiting to the idea that the unitary operation is just a basis change essentially turns us back to the Schrödinger picture where the vectors evolve and the operators stay they same

that some interpretation is generally possible doesn't mean you should always actually choose it

I was wondering that one cud still calculate the partition function of a qft on a minkowski spacetime with a periodic time dimension. Becuz the partition function does not care about initial value problms, and is merely a sum over all configurations.

But idk what this paritition function wud reveal about quantum physics on a periodic time

It is fine as a mathematical object, im having trouble giving it a probabilistic Interpretation

@ACuriousMind Looks like there is a section on Positronium using the Bethe-Salpeter equation in L&L 4. But yes, it looks like there is some sort of approximation going on

This looks interesting

It's crazy how the high school chemistry syllabus has things like the results from statistical mechanics, advanced atomic structure, different types of realised bound states (chemical bonds), the Pauli exclusion principle etc. meanwhile in high school physics, essentially it's just the stuff from Newton

Even the biology syllabus is horrendously complicated in the last 2 years

i see @ACuriousMind this clears it up !

At what point is it possible to learn about AdS/CFT?

never

CFT is Yoda CTF

I found my new favourite thing

Positronium

L&L 4 shows how to calculate the difference in energy levels just using QED

Hydrogen would be my favourite thing if the proton was fundamental

So it's handy for me since I don't want to believe in anything other than the electron, anti-electron and photon

What about Quarks, some people are superstitious about them lol

I would believe in them if they had a better name

Feynman called them Partons

Well them and Gluons

$Z_1, Z_2, Z_3, Z_4, Z_5, Z_6$

all i'm seeing are z's

must be tired

=]

@ACuriousMind Do you know of a resource that teaches linear algebra from a category theory perspective? if that makes sense :P

When I started physics many years ago I was so upset that they were teaching us non-latest Math stuff lol

But category theory?? :) Isn't that a bit too far? No I'm kidding I know very little about this

physics and math go hand in hand :P

the more you know of math, the better equipped you are

@Obliv agreed. But I think of it like this: You can come to a car garage with the perspective of a car enthusiast or that of a car mechanic. In physics courses it always feels like, especially at the beginning, students are encouraged to be more enthusiasts than mechanics, so that the Physics will get the main focus, and not the proving of theorems, etc.

The mechanic wants to go inside all the little rooms and inspect the tools and open the engines, etc, etc. But the race car driver (better analogy that way...) wants to get to the race and the car is just a tool

On the other hand, we know that often the driver gets the car into situations that the mechanic never thought of ^_^

I like this analogy, it extends pretty well lol

so good to be back :)

@SillyGoose I don't know one off the top of my head, but there are people who teach many of the constructions of linear algebra in terms of their universal properties (e.g. define the universal property of the direct sum, then prove its existence and uniqueness), that's probably the kind of stuff you're looking for

my first-semester LA course did that but I'm not sure if it followed any particular resource (and the one I think it might've followed - Lorenz' Lineare Algebra I - seems to only exist in German)