The h Bar

1:26 AM

@ACuriousMind yay monodromy groups

2:05 AM

@ACuriousMind I understand what is meant by non abelian stokes theorem and that's the way I see the claim that the connection is fully specified by it's monodromies. However what is the precise formulation of said theorem

naturallyInconsistent

@Semiclassical What else are you trying to bombard? The electrons are just there, they will do their thing, but it wont be interesting to nuclear physics. Photons will also be there, doing their thing.

Semiclassical

fair enough

naturallyInconsistent

@imbAF yes, e.g. "momentum eigenstates" of the free particle Hamiltonian. Or the continuous spectrum, electron going to infinity, part of the Hydrogen atom

naturallyInconsistent

2:58 AM

note that, by the fact that they are unbound, they are not normalisable and thus do not actually live in the Hilbert space. They live in Rigged Hilbert space, and are a generalisation of "states". Actually acceptable quantum states still have to be normalisable, and thus cannot be a specific stationary generalisation-of-states

Relativisticcucumber

@ACuriousMind i cant even imagine living in a society that not only believe in these values but is able to collectively embody this in their actions. that seems to be such a huge privilege.

but that is great

Silly Goose

4:12 AM

let the structure group’s lie algebra be a matrix lie algebra. Then, what is the meaning of $dg$ in a gauge transformation?

naturallyInconsistent

4:34 AM

@Relativisticcucumber Actually, that is the hooman norm. Hoomans are social creatures and the surviving civilisations are all social in nature. Not at all like snakes. It is the capitalists that are deviant

Silly Goose

5:31 AM

the index form of the lie algebra valued $3$-form $A \wedge dA$ is like $T_a T_b A^a_i \partial_j A_i^b dx^i \wedge dx^j \wedge dx^k$, right?

also why do people often omit the differential forms? can we replace them with a levi-cevita symbol or something?

(for the special case of $3$-forms)

(1) the differential form part of these lie algebra valued form quantities gives rise to a coordinate labeled antisymmetry. (2) this makes the whole quantity antisymmetric under coordinate index transpositions. (3) the levi-cevita symbol does this to tensors as well. (4) just replace $dx^i \wedge dx^j \wedge dx^k$ with $\epsilon^{ijk}$ and call it a day?

darn when there's commutators and anti-commutators what other brackets can i use in my expressions other than $()$ D:

only bigger $()$s...

and then in second line first term, is witten just explicitly writing out the antisymmetric part of the term?

because we could also just write $A_i\partial_j A_k$?

naturallyInconsistent

5:51 AM

@SillyGoose this is 3D space? If so, yes, the levi-civita symbol and the differential volume form are strongly related to each other.

Silly Goose

@naturallyInconsistent right in 3D

naturallyInconsistent

Well, if the author assumes that readers are not versed in differential forms language, this is a possible swap. But it seems like the author is assuming the opposite, that the readers already know the usual differential forms notation. After all, if you have an integral of A wedge A wedge A, without the integration element, then it means that A is itself a differential form. i.e. the first line is necessarily in differential forms notation, and the 2nd line is its coördinate expansion

Silly Goose

oh i see the relation is triple wedge goes to $\epsilon^{ijk}/2$ and witten's explicit writing of the antisymmetric part of the first term makes no difference.

Silly Goose

6:16 AM

bruh why do these notes call computing the change of the chern-simons action a simple exercise

naturallyInconsistent

@SillyGoose just like how a theoretical physicist's training consists of ever higher sophistication of the treatment of QHO being considered simple, and of a HEP physicist considering ever heavier massive particles as massless Nambu Goldstone bosons.

More Anonymous

Is there a distribution function which properly captures exoplanets?

More Anonymous

6:39 AM

Can I use this https://physics.stackexchange.com/a/811709/150174 to calculate the probability of life using empirical probability of parity symmetry?

0. Evolution is a process that assigns a probability that life can appear on any scale
1. Assume there exists an action which time evolves to give almost parity symmetric organisms and fit the proababilities based on that from earth
2. Can we use scaling arguments from FLRW metric + distribution of exoplanets + parity symmetry to find probability distribution of life habiting exoplanets?

Just some thoughts

I have to think harder on this

Conversation would help me clarify my thoughts

Actually FLRW metric + parity symmetry arguement = distribution of exoplanets?

More Anonymous

7:01 AM

Actually it would be cool if the distribution of exoplanets obeyed the same parity behavior

Ryder Rude

7:50 AM

hi

Relativisticcucumber

9:36 AM

@ACuriousMind since you are my adopted father does that mean i can become german

Mr. Feynman

9:47 AM

Can I be your brother? I want to be German too

Looks like ACM went to get milk

vengaq

11:19 AM

Hi @JohnRennie ! I would like to ask you a question about one of your stack exchange posts (https://physics.stackexchange.com/questions/367083/radiation-from-cosmological-horizons).

I was having a conversation in another physics forum about horizons (like the event horizon of a black hole, or a cosmological horizon) emitting Hawking radiation and I mentioned that if the universe keeps an accelerating expansion there will be a radiating cosmological hoizon (as the universe approaches a de Sitter space) therefore culminating in an asymptotic non-zero temperature.

John Rennie

@vengaq Hi :-)

The radiation does not come from the horizon, just like Hawking radiation does not come from the black hole horizon.

Your correspondent is quite correct that particles emitted from the cosmological horizon would take an infinite time to reach us, but since the particles don't come from the horizon this isn't a problem.

John Zimmerman

11:44 AM

Is it possible in GR to glue the boundary of a closed subset of a spacetime? What I mean is that can you glue 2 time-like separated leaves of a Cauchy foliation. I can't imagine that the resulting quotient space would be another subset of a spacetime?

More Anonymous

12:22 PM

@RyderRude hey,n

Ryder Rude

12:32 PM

@MoreAnonymous hey

Ryder Rude

12:43 PM

@JohnZimmerman i think it wud produce CTCs

John Zimmerman

@RyderRude i think you're right

would be more of a Riemmanian geometry construct

More Anonymous

2:18 PM

@RyderRude Any book recommendation?

Ryder Rude

2:54 PM

@SirCumference hi. what math fields have the most enjoyable proofs

@MoreAnonymous what r ur interests

@MoreAnonymous read Nakahara's book if u r interested in topological invariant groups associated to manifolds

bolbteppa

Don't read that book unless you want to spend a year learning how to re-state simple things you already know in big words

Ryder Rude

but u recommended it!

i find it really good becuz it's informal and doesnt go around proving tiny details @bolbteppa

bolbteppa

Although I would recommend GSW, twitter hype on Polchinski would not be a bad thing to fall for, these and these lectures follow it

Ryder Rude

these lectures would take decades to watch

bolbteppa

It would take just over 2 days if you sat there consecutively to watch the first set, the second set do the same material I don't know where the differences are

The real problem is when you get stuck on something simple for a week/month

The way he does the lightcone particle should give anybody a weeks worth of pause

Ryder Rude

3:04 PM

i sometimes find books to be too comprehensive. is it betr to follow a university course? @bolbteppa

i guess books are like tree branches and courses are more linear and focused

@bolbteppa is this analogy correct

bolbteppa

The ideal is a set of lectures where the lecturer follows a book but explains all the missing details and makes it all incredibly obvious and does it in a way that explains why other sources do things differently, good luck finding that

Ryder Rude

oh

i lose attention while watching videos and hav to rewind

Semiclassical

my attempt to make a mass spectrometer with Tikz accidentally came out a lot more questionable than i intended

bolbteppa

If I asked Skynet to make a diagram like that for me, it would take forever to get it right

Semiclassical

tbh i mostly stole it

tikz.net/velocity_selector

i wanted to show two trajectories, one clockwise and another counterclockwise

and accidentally made it more phallic than intended

bolbteppa

3:16 PM

I can now see it another way too...

Semiclassical

one thing i did find myself wondering about. the setup shown above is the one you usually see in intro physics books, and it includes the velocity selector before the magnetic sector

but most other mass spectrometers i've seen seem to go directly to the magnetic sector

is it just that the intro physics books use the velocity selector b/c it's an easy example for the Lorentz force?

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