/sci/ - Science & Math

Tensors don't show up until page 15
Calculating components of a tensor is at the end

The flood blocker is lame...

>>1115475
WTF? do they use this shit anywhere? whats wrong with the standard tensor notation? with the subscripts and superscripts, it seeems pretty easy to me, at leasy easier then this!

>>1115505
You of little faith.
You haven't even seen the notation yet! Wait until page 15

It's cake compared to the usual notation.

I lied, tensors show up on page 13

And here is one place where the notation really shines over the standard notation

I don't think anyone will care if I go away for half an hour - this is a good place to take a break

For tensors, this notation doesn't seem to me to be much better than indices, but for spinors and for Lie algebra representations, it's wonderful. The Fierz identity is so much easier to use graphically.

MAKE MORE TUTORIALS
MAKE PDFS
MAKE

>>1115575
>>1115475

Yeah, this notation is bullshit. Im sticking to the standard tensor notation, its much better, neater, and understandable.

Thank you, OP. I've seen this notation sometimes, and never quite gotten it, so nice to read a good explanation. However, abstract indices works kinda fine too imo.

>>1115595
AGREED, WAY TO DO SOMETHING POINTLESS OP!

>>1115595
>understandable
Took me long enough to like index notation.

The rest of this is on how to compute components of tensors.

>>1115475
rapidshit plox!

>>1115703
Eh, if you want it up on Rapidshare, you can do it.

Dissecting a tensor with a Mathemagician Tool

Cute tensors. Wouldn't have thought to encounter these.
I'll probably mail you in a few days once your tutorial is finished, I think it's an interesting alternative way of dealing with tensors. (... but I'm still wondering whether it has some practical use. Any info on that?)

OP, they have this thing called Powerpoint now.

You should look into it.

And this is the last one.

The topics not included are derivatives and Lie Algebras. I don't have anything written on those yet, and it will probably be a while until I do. I probably won't be posting them here unless people really want them (but it seems like there are only a handful of people who would care)

>>1115763

If you're doing stuff with a whole bunch of tensors, lot's of contractions, etc, then the diagrams are much easier to look at and work with.
Of course there's nothing that you can't do with the original notation. I just like looking at diagrams much more than a long line of algebra.

>>1115774
I'd have to draw the diagrams by hand anyway. Powerpoint would just make this harder!

>>1115763
I've also posted this at PhysicsForums I'll be putting any new pages up there (new pages probably won't be for a while)

archive

>>1115763
I don't think this method will turn out to have any practical use. I think it'd be a great way to teach the concepts behind multilinear algebra. I could be wrong, though; a friend of mine started working on a diff.geometry notation that I never thought would work, but she's using it fine. In practice, I find alternate notations are more of a concept/sanity check than a way to do calculations or proofs.

>>1115960
This guy Predrag Cvitanović used the notation to find a new characterization of all of the Lie groups. Apparently they all fall out in some nice hierarchy in terms of invariants of the diagrams, even the exceptional groups.

There are definitely applications, but aside from nicer notation, they're pretty abstract stuff.

Of course Feynman diagrams are exactly tensors written in this notation and Physicists find them very useful.

>>1116395
idk about Cvitanovic's stuff, but I do know Feynman diagrams. At least in that case, I stand by what I said: Feynman diagrams are an awesome way to check concepts and sanity, but they don't necessarily make the calculations any easier. Certainly not until you've done the calculations enough to know what the Feynman diagrams are telling you in the first place...

But that's the caveat with new notation, isn't it? It's new. I'm skeptical that it'll work in practice, but that's because I haven't tried. And it'll take practice to get used to.

Awesome