Re: Order of indices in tensors...
From: Danny Ross Lunsford (antimatter33_at_yahoo.com)
Date: 08/26/04
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Date: 26 Aug 2004 05:07:19 -0400
"Flip Tomato" <flipt@stanford.edu> wrote in message news:<cgbmkh$2rv$1@news.Stanford.EDU>...
> Hello--I'm doing some intro-GR (using Carroll's new book), and I am confused
> about a subtle point:
>
> What is the significance of the order of indices in a tensor? I understand
> that the convention is for upper indices to sum with lower indices and vice
> versa when the tensor acts on the appropriate object, however, what is the
> significance of having the upper index listed first or the lower index
> listed first (horizontally)?
It's not the order but the symmetry that is important. The order can
be thought to represent the (arbitrary) choice of independent
directions in a local frame, while the symmetry properties represent
persistent geometrical facts about the objects they represent.
Particularly important are totally antisymmetric tensors (changes sign
on interchange of any two indices). These represent primitive "space
elements" - line segments, surface elements, volume elements etc.
-drl
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