/sci/ - Science & Math

[Anonymous No.9815929]

what does this means eh?

[Anonymous No.9815932]

>>9815929
It means the owner is a pretentious douche.

[Anonymous No.9815933]

>>9815929
>not recognizing the Lagrangian

[Anonymous No.9815934]

>>9815932
oh yeah defenitely

[Anonymous No.9815943]

>>9815933
I mean I recognize the first term as the Lagrangian for electromagnetic field. I guess the last one is the external potential. I don't recognize the other.
h.c. might be plank constant * light velocity but I'm not quite sure why is this in the Lagrangian.

[Anonymous No.9816349]

>>9815943
Its the combined one for fermions, electromagnitism, the weak force, quantum chromodynamics, and the higgs mechanism (the last term is part of that). + h.c. stand for hermishian conjugate of the previous term

[Anonymous No.9816351]

>>9815943

+h.c. means "+ (hermitian conjugate)" and it's a notation you see in high energy theory contexts

this looks like some generic field lagrangian

[Anonymous No.9816361]

It means u have no mates lol

[Anonymous No.9816378]

https://en.wikipedia.org/wiki/Feynman_slash_notation

[Anonymous No.9816668]

>>9816349
>quantum chromodynamics
>no Lie indices on F
Why are undergrads SO quick to disclose their stupidity? It's the QED Lagrangian with dynamically generated electron mass.

[Anonymous No.9816706]

>>9816668
>Why are undergrads SO quick to disclose their stupidity? It's the QED Lagrangian with dynamically generated electron mass.
Its a retarded way to write it, but that is (supposed to be) the complete standard model. CERN even calls that the standard model, a quote from them:
>The top line describes the forces in the Universe: electricity, magnetism, and strong and weak nuclear forces.

They suppress the index on F and a bunch of other things to get it in that compact form, they suppressed 2 indexes om the second term as well (if you compare notation with the 3rd line). What I dont get is why they then left in some of them instead of just writing F^2 if they want to go full compact. IM guessing they were going for s specific level of complexity to look simple yet interesting.

[Anonymous No.9816720]

>>9816706
>but that is (supposed to be) the complete standard model
About yhe mug?
They're fucking idiots if they suppress the Lie indices but not the spacetime indices. Suppressing spinor indices I understand, since physicists always use the same change spinor bundle, but Lie indices literally tell you the gauge force carriers, hence without them you don't know what the Lagrangian is trying to model.
>of just writing F^2
You mean F*F? F^2 is the Chern-Simons term which has NO dynamics and hence can't mediate anything. That's the pion/axion term.
>IM guessing they were going for s specific level of complexity to look simple yet interesting.
And they've failed, sort of like your post.

[Anonymous No.9816775]

>>9815933
>not knowing the difference between Lagrangian and Lagrangian density

[Anonymous No.9816779]

>>9816720
>You mean F*F? F^2 is the Chern-Simons term which has NO dynamics and hence can't mediate anything.
I have seen people write F^2 for FmunuFmunu in papers, how is using that notation any worse than suppressing the Lie index? stop trying so hard to pretend youre smart. If you dont like it go complain to CERN.

[Anonymous No.9816871]

>>9816779
>I have seen people write F^2 for FmunuFmunu
Then they're wrong. F^2 is the curvature, 2-form which means you can't integrate it over the (presumably) 4D manifold M unless you take the trace over form indices. *F is the Hodge dual of F, which is a 3 form, so you can integrate F*F (which is a 4-form) over M without taking the trace. Learn differential topology before posting, retard.
>how is using that notation any worse than suppressing the Lie index?
Because it's wrong. Suppressing the Lie index is not the problem, the egregious misuse of proper mathematical notation is.
In addition, in Yang-Mills theories the gauge groups are taken to be compact and connected, but otherwise arbitrary. This means that writing in explicit Lie indices doesn't do jack shit for you since you don't even know what the basis for the Lie algebra is. Besides, in actual mathematical literature, which I'm sure you have never touched in your short undergrad life, the gauge group that the Yang-Mills theory studies is clear from context, and it is only strictly needed for physical interpretations.
>stop trying so hard
I'm trying very little, and it seems to be more than sufficient in sitting your stupid ass down and make change. Don't ever reply to me again until you've learned enough to not embarrass yourself, dumbass freshman.

[Anonymous No.9816894]

>>9816779
>I have seen people write F^2 for FmunuFmunu
Then they're wrong. F^2 is antisymmetric in the form indices while F*F is symmetric (with the Hodge dual), meaning that the Hodge pairing is only non-denegerate for F*F but not F^2. Learn differential topology before posting, retard.
>how is using that notation any worse than suppressing the Lie index?
Because it's wrong. Suppressing the Lie index is not the problem, the egregious misuse of proper mathematical notation is.
In addition, in Yang-Mills theories the gauge groups are taken to be compact and connected, but otherwise arbitrary. This means that writing in explicit Lie indices doesn't do jack shit for you since you don't even know what the basis for the Lie algebra is. Besides, in actual mathematical literature, which I'm sure you have never touched in your short undergrad life, the gauge group that the Yang-Mills theory studies is clear from context, and it is only strictly needed for physical interpretations.
>stop trying so hard
I'm trying very little, and it seems to be more than sufficient in sitting your stupid ass down and make change. Don't ever reply to me again until you've learned enough to not embarrass yourself, dumbass freshman.

[Anonymous No.9816932]

>>9815933

lagrangian what?
are you fucking stupid?

[Anonymous No.9816942]

>>9816932
Lagrangian function, if you want to be pedantic. Everyone who knows what it's for just calls it the Lagrangian because it's faster to say it that way.

[Anonymous No.9816951]

>>9816894
kek, direct your autism at CERN please, im just telling you what they wrote. mathematical notation is a social construct anyway, it cant be wrong if that's the way they define it.

[Anonymous No.9816960]

>>9816942

no its not, i know what it is but i've never heard anybody call it "lagrangian" , the lagrangian is the function that you get if you apply the lagrange multiplicator to a function
it's also high school stuff over here hehexD

[Anonymous No.9816970]

>>9816894
Or you know, they just mean |F|^2 .


Also
> Learn differential topology before posting, retard.

Hodge theory is very clearly differential geometry.

[Anonymous No.9816978]

>>9816960
>Lagrange multiplicator
Shame you didn’t pay attention in high school, then

[Anonymous No.9816980]

>>9816960
wat

[Anonymous No.9816983]

>>9816978
>>9816980

stfu you fucking apes

"For the case of only one constraint and only two choice variables (as exemplified in Figure 1), consider the optimization problem

maximize f(x, y)
subject to g(x, y) = 0.
(Sometimes an additive constant is shown separately rather than being included in g, in which case the constraint is written g(x, y) = c, as in Figure 1.) We assume that both f and g have continuous first partial derivatives. We introduce a new variable (λ) called a Lagrange multiplier and study the Lagrange function (or Lagrangian or Lagrangian expression) defined by

{\displaystyle {\mathcal {L}}(x,y,\lambda )=f(x,y)-\lambda \cdot g(x,y),} {\displaystyle {\mathcal {L}}(x,y,\lambda )=f(x,y)-\lambda \cdot g(x,y),} "

[Anonymous No.9816991]

>>9816983
>>9816960
Its the same god damn thing you retard. The L is the Lagrangian, it includes all the constrains of the physical system, in it as Lagrange multipliers, you put it in Lagrange's equations to get the equations of motion in classical mechanics, or do path integrals in quantum mechanics.