12:57 AM
@DIRAC1930 Why not ?

6 hours later…
7:02 AM
@MoreAnonymous haha :-) I guess you don't remember, two years back probably, you had posted a link to your soundcloud, it already had your name :P XD

7:20 AM
@RewCie Shoosh :P

2 hours later…
9:37 AM
No, the gauge group is independent of flavour - the quotient comes from the fact that the quantum numbers of the SM particles match up nicely so that transforming the fields by the $\mathbb Z_2\times\mathbb Z_3$ centre of $\mathrm{SU}(2)\times\mathrm{SU}(3)$ can always be undone with an appropriate $\mathrm U(1)$ rotation. So there's a $\mathbb Z_6$ invariance here, but nothing to suggest that we should quotient out by it or one of its subgroups.

This is because correlators of local operators in SU(N) gauge theory remain the same when you mod by a central discrete factor - you have to use

9:56 AM
Alright
"We learn in kindergarten that we should take $$G = U(1) \times SU(2) \times SU(3)$$"
Learning about theoretical physics is mostly a way to be condescending to other physicists

3 hours later…
1:17 PM

2 hours later…
3:11 PM
How do people usually bridge the gap from standard grad-level courses to research papers in high energy theory?
It seems like there's a huge gap

depends on the paper, I guess
there's a variety of books on the many topics of HEP
Usually relevant books will be mentionned in the bibliography

I know but they seem to be either entry-level textbooks or full-on monographs

@DIRAC1930 start reading, then follow the citation trail/look up review articles for the stuff you don't understand

also you can ask here I guess
otherwise you may have to climb back up the chain of bibliography
until you find the paper that introduced the concept

it's rare that you need to read a full book to appreciate an argument and you need to let go of the illusion that you can understand every detail of every paper you read
knowing what you do need to understand in detail is pretty crucial to not get lost in the entire physics literature of the last century :P

3:18 PM
Also remember that HEP is mostly nonsense

I feel let down by QFT lol

Don't think too hard about it

@DIRAC1930 QFT is probably the first thing one encounters during a physics degree that's not "settled science"

A lot of times it's just "That sounds like a reasonable enough idea"

I mean, we have a pretty good grasp on it, but it's very far from the solid foundations e.g. classical mechanics rests on

3:20 PM
I wish I knew more classical field theory

both with respect to the mathematical underpinning and with respect to having figured out the proper pedagogy

There's a lot of QFT methods with historical roots being basically "Well let's see what happens if I pretend that this works"

Is canonical quantization one of them or is that fully rigorous?

"canonical quantization" covers a lot of things

canonical quantization isn't a fixed procedure, it's what physicists call the kind of quantization where you don't think too deeply about it :P

3:23 PM
Although historically canonical quantization was basically "Well things are waves, waves are like $\exp(ixp)$, so the momentum is gonna be like $i\partial$"

When I learnt QFT (badly) the first time, the lecturer started just by changing the Fourier constants to operators without saying anything about it and I was like wtf

well but that's just how you do it in QM
suddenly $x$ and $p$ are operators

Thats true

no one goes and derives the Stone-von Neumann theorem or something like that before doing QM

But theres many lectures on the Heisenberg uncertaintly relation etc
At that point, I didn't know what a Fock space was
So I had no idea why he was doing what he was doing

3:25 PM
Also the Klein Gordon equation was like a horribly handwavey argument about $E^2 = m^2 + p^2$

@DIRAC1930 he was trying to get a quantum theory, and you get a quantum theory by turning things into operators and see where that goes!
sure, that's not rigorous, but that's how physics is generally done

Lol I know but for someone who hadn't seen much QM before, I was very confused

well, that's a problem - I do believe that one shouldn't try to teach QFT to people who don't have a firm understanding of QM
because it'll be impossible for them to tell which of these strange things is because of "quantum" and which is because of the field part

@Slereah But isn't the Schrodinger equation derived using the non-rel version of that?

@Slereah that was brutal

3:28 PM
it's similar to doing QM with people who have never seen classical Hamiltonian mechanics - they usually get very confused because they can't tell which ideas are quantum and which are just because of the Hamiltonian viewpoint
neither of these confusions is a problem with rigor, it's just a problem with the course structure at the places where that happens

I think this is the problem when going to a school isn't strong in theoretical physics
Or doesn't have a theoretical physics program

IIRC we were taught QM before Lagrangian mechanics
Not the best idea

But if you go to a school that doesn't have many researchers in theoretical physics, I doubt they will be able to teach Lagrangian mechanics in much detail

I'm not asking for the fanciest course on the topic
But just "The Hamiltonian generates time evolution" would be enough

Yeah I wasn't taught that in undergraduate either

3:31 PM
and also as I said, do something like a classical probability distribution on your initial conditions
Your object is at $t = 0$ on some normal distribution for its position
Evolve that with the Hamiltonian
See what the error is evolving like

Also, I wish QFT courses didn't waste so much time on scattering experiements
I know I'm probably in the minority on that

Well as I said
Hydrogen atom, step potential
Also look up QFT for quantum optics
It's a lot of non-scattering stuff

Yes QFT in condensed matter is probably the best place to start

I don't recommend condensed matter but only because I hate it

I hate it too
Except this SYK model seems interesting

3:35 PM
it's not wasted - the majority of QFT applications is in hep-th, and the majority of hep-th experiments are scattering experiments
it's a bit unclear why you might want to learn QFT if you're interested in neither hep-th nor cond-mat, actually :P

I know but there could be an extra course on scattering
I felt the things that seemed important such as Wigners Classification were just rushed over in 30 mins
I'm interested in hep-th but I don't know enough
I think I'm more interested in the idea of hep-th during the 30s or something

ah, you want to build nuclear bombs, gotcha

@ACuriousMind “formal quantization” would almost be a better name for it

Lol
What do people thing of Eric Weinstein?

I don't think about him, usually :P

3:43 PM
I think about him probably once every 2 days lol
@ACuriousMind Who's the most famous physicist you've spoken to?

I...don't think I should rank my acquaintances that way

I want to say I’ve seen Frank Wilcek give a talk. That’s probably the “biggest” name that comes to mind

I'm also not a professional physicist so you're probably imagining far more contact with physicists than I actually have

Amusingly, I do have semi-regular contact with one of Bohm’s students..,who has subsequently gone on to do work which is not Bohmian in the slightest

Is it easier to get a place doing a Ph.D. in string theory in Eastern Europe or Russia compared to the US or UK?

4:02 PM
I sorta doubt you’ll find anyone with the expertise to answer that question in this chat

Okay

4:19 PM
Why is it that we can measure charge?
'A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated quantities can be measured, such as charges, energies, and velocities. '
A gauge theory is a type of theory in physics. The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). Modern theories describe physical forces in terms of fields, e.g., the electromagnetic field, the gravitational field, and fields that describe forces between the elementary particles. A general feature of these field theories is that the fundamental fields cannot be directly measured; however, some associated...
Around the 3rd/4th line
Or is this again a statistical argument

no, that's a gauge argument - e.g. the 4-potential in EM is gauge-variant, and so you can't measure it
since only gauge-invariant quantities are physically meaningful

Why do you think we can measure charge
In the end we can only measure directly what we can sense
Everything else is indirect

I'm not entirely sure why we can measure anything tbh

You don't measure temperature, you just see the indicator go up on a thermometer
Hopefully that is temperature

actually, did you read the paragraph to its end? It explains that it means that the stuff we can measure is precisely the gauge-invariant stuff

4:23 PM
Well gauge is even more nonsense than other quantities

this isn't some philosophical argument about how measurement works, it's a very straightforward claim of what things you can "measure" in the very ordinary colloquial sense of the word, namely that of having a device that outputs some number for the measured quantity

Where is my gaugometer

Okay forget about gauge invariant theories

note that it's also not a quantum argument, gauge theories are also a classical notion
@DIRAC1930 ...why did you cite the intro to the article "Introduction to gauge theory" if you don't want to talk about gauge theories? :P

4:25 PM
How do we know if an operator corresponds to a physical observable

spoiler: I like talking about gauge theories :P
@DIRAC1930 what's your definition of "physical observable"?

@DIRAC1930 usually you kind of guess at it from what you know about the experiments
And usually it's kind of indirect

I think experimentally if you would want to show that an indirect measurement actually means what you think it means, you have to find a way to make another experimentally verifiable prediction based on what you expect the indirect measurement is telling you

You don't really measure spin directly in QM experiments
You see where the particle goes in some systems

The only certainty you have is energy correct?
everything else is uncertain

4:28 PM
no? and energy doesn't have to be certain either
$|E_0\rangle+|E_1\rangle$ does not have a definite energy (unless $E_1=E_0$ ofc)

There's no energiometer either

Is the equation not rendering for anyone else either?

see Mathjax in chat in the upper right
different interpretations have different views on this, of course. for instance, Bohmian mechanics insists that everything is secretly a position measurement and grounds its ontology in those

What is an abelian symmetry?

I must be blind, I can't find the mathjax option

4:31 PM
it's in the room description in the upper right
right above the icons

@DIRAC1930 A symmetry whose symmetry group is Abelian

Oh I see, I was looking for a menu option
thanks
Abelian symetry means you can apply the binary operations of a group communatively

Also, for operators vs. observables, see physics.stackexchange.com/q/373357/50583, there's a pithy answer by me and a much more detailed one by Valter Moretti

AB = BA

So say for a particle in a 1d box, how is parity an abelian symmetry?

4:32 PM
a 1d box?

if you've only got one operation, then it's automatically abelian
b/c what would it need to commute with?

Okay, so from Schlurs lemma, all abelian irreps are one dimensional
So if I have a set $H, N, O$
which all commute

...how are you jumping from "what does Abelian mean?" to Schur's lemma???

does that mean $O$ is conserved for each individual particle

@DIRAC1930 ...do you mean that $N$ is a number operator?

4:34 PM
yes

I think technically if you performed an experiment with a variety of prepared states that spanned a lot of the Hilbert space, you could maybe reconstruct the operator for this
But I'm not sure
I don't know much about QM epistemology
There are ways you can do such things in GR anywya

the constraint would have to be the group being $\{\mathbb{I}, O, O^n\}$ and then for some $n$, $O^n= \mathbb{I}$ right for it to be a finite group?
If that were the case, each number state would be quantized with some value $o^n$ where $o^n$ is the eigenvalue of $O^n$
right?

what

Is 𝕀 supposed to be the ideal?

I have no idea what group you're talking about

4:39 PM
$\mathbb{I}$ is the identity

Algebrist here, not a physicist

I'm trying to form a finite abelian group with the operator $O$
for parity it would be $\{\mathbb{I}, \hat{P}\}$ right?

well, whether it's finite or not depends on whether $O^n = 1$ for some $n$ as you said. But why are you trying that?
@DIRAC1930 yes, parity without anything else is just the two-element group ($\mathbb{Z}_2$)

I'm trying to figure out how I can form a basis of states such that for each number operator state, there is a definite conserved charge $O$
therefore each individual particle, would carry a conserved charge

and Z2 is as abelian as one can get, unless you count the group of 1 element as such

4:41 PM
@DIRAC1930 since $O$ and $N$ commute, each eigenspace of $N$ forms a subspace that maps into itself when $O$ is applied to it

So if I understand correctly, you have one operator and you want to form a finite group right?

and so you can just apply the spectral theorem to the eigenspaces of $N$ to get a basis $\lvert n,o\rangle$ that are eigenstates of both $N$ and $O$

But $O$ on it's own doesn't form an abelian group

why does it have to form an Abelian group?

sure it does

4:42 PM
Thats true, it doesn't have to

$O^n O^m=O^m O^n$

this is just spectral theory for a single operator

if you generate a group using a single generator, it'll always be abelian

So if $\{H,N,O\}$ form a complete set of commuting observables, each state with definite number carries a definite conserved charge

order can't matter when you're talking about powers of a single generator

4:44 PM
I don't know how to construct your operator, but all I can tell you is that if you want it to be finite, you should be able to start at 1 and repeatedly apply the operator a finite amount of times and then return to 1

@DIRAC1930 sure
I'm confused what this has to do with Abelian groups or Schur's lemma, you seem to be jumping very randomly between stuff :P

How do I make one particle carry exactly one unit of $O$

diagonalization in general

I don't know what that means

Like in electrodynamics, 1 electron has a charge of exactly $e$

4:46 PM
In general, the spectrum of $O$ might be something like $1,1/2, 1/4,1/8,\dots$, there doesn't have to be a "unit"

just because an $O=1$ eigenstate exists, doesn't mean there's going to be a simple way to compute it

Thats what I was worried about

other than just "demand that $(O-1)|1\rangle=0$"

So I need $O$ to only have $1$ eigenstate?

what?

4:46 PM
you don't start with a random operator and try to make it into a charge
you start with a physical theory and discover it has charges

I get that
I realised what I'm trying to do was already done for $S_z$

the discreteness of electric charge arises from the charge classifying the representation of the EM gauge group $U(1)$ the particle transforms in, it's not something inherent to "conserved operators"

Sorry, I was using that as a bad example
non-rel spin is probably what I'm trying to do

I still have no idea what's going on, but if you're happy that's fine :P

Okay what I'm trying to figure out is how to more rigorously show that $<Q>$ is conserved for the GCE
where $Q$ is a conserved charge

4:53 PM
ew, statistical mechanics :P

I thought that maybe if you could show that each particle carries a conserved charge, then if you assume $<N>$ is conserved, then $<Q>$ follows
Can conserved charges be macroscopic?

a question i don't know: how does the grand canonical ensemble work if you have $[H,N]\neq 0$
(one possible answer, of course, would be "it doesn't")

I think colloquially in the quantum case GCE is defined with $p_i = e^{\beta E_i + \sum_i a_i Q_i}$
I think in the prequantum days they didn't have to worry about other conserved charges

i mean, I can still write $Z=\operatorname{tr}e^{-\beta(H+\mu N)}$
i'm just not sure if that's sensible when $[H,N]\neq 0$

$N$ in the numerator doesn't say anything about $[H,N]=0$
It appears when you have $<N>$ being conserved
I think there may be a subtle difference

5:03 PM
a fun looking paper

Those diagrams look cool

i've seen a few attempts to do E&M with differential forms
but it's never really taken off

It is pretty standard
Well, standard in some circles, I should say
Engineers aren't big on forms

The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist at Leiden University, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force F = − V ′ ( x ) {\displaystyle F=-V'(x)} on a massive particle moving in a scalar potential V ( x ) {\displaystyle V(x)} , The Ehrenfest theorem is a special case of a...
So perhaps you need the equation in the 2nd box to hold
which seems unlikely if $[H,N]\neq 0$
but I don't really know anything

3 hours later…
7:54 PM
Things get so tense when you meet physics fanboys who have opinions about quantum gravity
Calm down, theorists are allowed to work on something even if it's not the metaphysical truth

8:13 PM
I wish I knew enough to understand the problems trying to quanitze gravity

there's no lack of problems

Are the problems more on the gravity side or the quantum side?
What did Dirac think of string theory?

It was a bit of a delta from the norm, but it was functional and fully braketed the problem.

@DIRAC1930 Dirac died in '84, string theory in the modern sense didn't really exist at that point

8:32 PM
Why do we care about irreps and not just reps?

Reps are made of irreps
reps are also important, but they're not fundamental
@ACuriousMind there was string theory in the 70's!

@Slereah that's why I said "in the modern sense"!

Maybe not cool and modern string theory but still
All the basic ideas were there
also there was dumb stuff like pomerons or whatever

'84 was right on the brink of the "first superstring revolution"

if you look at a system of two scalar particles, that's a rep made of the two trivial irreps
things get more complex with higher reps

8:37 PM
And what does it mean to classify the irreps?

Well usually the irreps fall into only a few categories
depending on what group they transform with

@DIRAC1930 For semisimple groups/algebras, all reps are direct sums of irreps
so if you know all irreps, you also know all reps

although of course, you get weird behaviours
like spin $1/2$ reps combining to form scalar and vector reps!

@DIRAC1930 It means figuring out how many there are and what some basic properties are, e.g. "classifying" SU(2) irreps by the total spin $s$
values like $s$ that are constant on the irreps are related to the notion of Casimirs - the idea is to enumerate enough Casimir operators whose value then uniquely identifies an irrep and know what the possible values are.

Okay thanks

9:34 PM
2

The problem Consider a stochastic process with the following three properties: The process is Markov, meaning that $p(x_n,t_n|x_{n-1},t_{n-1},\ldots x_1, t_1) = p(x_n,t_n|x_{n-1},t_{n-1}).$ The conditional probability is p(x_n, t_n|x_{n-1},t_{n-1}) = \left[ 2 \pi \sigma^2 (1 - e^{-2 \gamma (t_...

halp

What does modern research in stat mech entail?

The prompt for this AI-generated art is "String theory diagram of the cohomology cocycle of the 2-connection co-field infinite L algebra in BV BRST gauge quantization"
Not the best representation of such

10:27 PM
What site is that on?

0

I have this question: Bomb attached to accelerating charge, as viewed from a co-moving frame? Now it was closed, and then it was downvoted. I do not understand why we are allowing downvotes (or any votes) on closed questions. But that is not the only question here I am trying to ask, rather, if a...

11:06 PM
@DIRAC1930 it's a huge field
I don't know if there is any good overview, but it's really huge, you'll have to be more specific. If you want to see some random topics you can have a look at the speakers of the last big statphys conference statphys27.df.uba.ar/index.html or a specific journal like iopscience.iop.org/journal/1742-5468
don't expect to understand much though