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/sci/ - Science & Math

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2689195 No.2689195 [Reply] [Original]

SUP /SCI/

Does anybody know the commutator of the co-variant derivative and a normal partial derivative? (Cannot be asked to wrestle with the Christ-awful symbols.)

THANKS

>> No.2689240
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2689240

BUMP

>> No.2689251
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2689251

>> No.2689285
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2689285

>>2689251
Thanks, but could I have it for rank two tensor. (Sorry should of said)

>> No.2689291
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2689291

when I think about it, probably D∂A=? is the part you have trouble with, so here it is.
You really just treat ∂A as a 2-form, ie. M_\{mu,nu}=(∂A)_\{mu,nu} and apply the rules you have in your script (or wikipedia)

>> No.2689309
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2689309

>> No.2689320

>>2689309
Thanks, it isn't as pretty as I thought.

>> No.2689324
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2689324

and lastly the commutator
(I hope you now don't want the tensor to be anti-symmetric or whatnot)

>> No.2689341

>>2689324
No, its cool. OPfag is going to equal the metric tensor anyway.

>> No.2689342
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2689342

>>2689320
the covariant derivative gives you the partial derivative and then one term per index involving chrisoffels.
On top of that you use a partial derivative on that which means some product rule.
What else did you expect than some 3 to 6 term expression?

>> No.2689361
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2689361

>>2689341
what?
you know that the christoffel connection is the one and only connection which eats the metric, right?
Thats the point of it, really.

>> No.2689390
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2689390

You're Welcome.

>> No.2689384
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2689384

Alle Menschen werden Brüder, wo dein sanfter Flügel weilt.

>> No.2689409

>>2689361
I know.

I'm not supposed to know that OPfag is the metric tensor yet though.

>> No.2689435
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2689435

Physics?? In my /sci/

>> No.2689436
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2689436

>>2689409
you're not supposed to know that OP is a fag?
But it's obvious, really.

>> No.2689460
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2689460

>>2689435
until now it could be considered pure Riemannian geometry.

>> No.2689464
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2689464

>>2689436
You set up a Mathematica visualization to do that...

<-- Also, the domain its valid for

>> No.2689479

Anyone got their hands on Mathematica 8? And is it worth a download?

>> No.2689489
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2689489

>>2689464
I don't understand.
and
>the domain its valid for
what does that mean?

>> No.2689522

>>2689489
http://en.wikipedia.org/wiki/Domain_of_a_function
>>2689479
Yes, it isn't a huge upgrade (apart from "Free-Form Linguistic Input" which I can't use because I've got a shitty pirated version.) Wavelet analysis is pretty cool.

>> No.2689537

>>2689489
oh, thanks for the link (...)
"the domain its valid for"
is kind of a tautologic expression, that's what I was saying

>> No.2689556

>>2689537
I'm not sure.
An if statement can produce an invalid result for things inside its domain.