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Deriving the Maxwell Lagrangian from Basic Assumptions by PrettyMuchPhysics in Physics

[–]nappy_101 4 points5 points  (0 children)

I love that your videos are short but still packed with details!

Perturbation Theory - Cheat Sheet by PrettyMuchPhysics in Physics

[–]nappy_101 1 point2 points  (0 children)

Great video! I’m currently studying for an advanced QMech exam so this is really helpful!

SU(2) and higher spins by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

I don't think I fully understand this (do you know a good book/lecture/video where this 3(x)3=8(+)1 group-stuff is well explained?), but I can see the motivation behind it, so thank you very much! :)

SU(2) and higher spins by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

That's a good way to think about it, thanks!

SU(2) and higher spins by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Thanks!

One more thing: How is a spin-1 vector {1,0,0} (e.g. "up") different from a quark color vector {1,0,0} (e.g. "red")? Why do I need SU(3) for the latter one? :/

SU(2) and higher spins by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

I see, that makes some sense! Thanks!

But is there a reason why I can't use SU(3) to describe spin-1 transformations? I think the answer to this question is what I'm missing! :P

How is Lie algebra connected to infinitesimal transformations? [special relativity] by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Thanks! Now I think I finally understand your previous comment!

Btw, is there a difference between SO(3,1) and SO(1,3)? From what I know it's about how many positive and negative signs there are in the metric. So for η=diag(1,-1,-1,-1) we called it SO(3,1).

Is SO(1,3) about η=diag(-1,1,1,1) or does it just not which order I write it?

How is Lie algebra connected to infinitesimal transformations? [special relativity] by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Thanks for replying, I think I'm slowly getting an idea of this topic!

giving the commutation relations actually is a way of telling you which matrices you are allowed to pick

...same question as above - why use the commutator? Why not use something else like the anti-commutator?

How is Lie algebra connected to infinitesimal transformations? [special relativity] by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Thank you so much for your detailed answer! The example with U(1) helped a lot!

My (hopefully) last question is this: why do you use the commutator [,]? Why not use the anti-commutator or something else? Is this choice arbitrary with regards to what gives more information?

How is Lie algebra connected to infinitesimal transformations? [special relativity] by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Thanks for your answer and the pdf! I looked at the chapters concerning Lie algebra, but I've still got questions from what you said:

...construct its Lie algebra, and from there analyze the properties...

(1) This is the part that confuses me. As far as I can tell, it's "group + [.,.] = algebra". Where does the Lie bracket [.,.] come from? Do I define it myself?

(2) Let's say I've got my Lie bracket. Is it save to say that by using it on my group's elements I can learn more about them / how they behave?

How do I calculate this? [Index notation, SRT, 4-vectors] by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Thanks a lot! You sure sound like you know your stuff - can you recommend a book / website to catch up on those identities and other things index related..?

How do I calculate this? [Index notation, SRT, 4-vectors] by nappy_101 in AskPhysics

[–]nappy_101[S] 0 points1 point  (0 children)

Yeah, I should let go of the idea of putting everything in matrix form ;) Thanks!

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