Mike_Fontenot
Jan6-09, 06:00 AM
[[Mod. note -- I mistakenly deleted this article's References: headers
when saving it from my inbox into my s.p.r articles-to-be-moderated queue.
I apologise to the author and other readers for this, and for the ensuing
loss of threading in many newsreaders.
-- jt]]
Theo Wollenleben wrote:
>
> [...]
>
>
And I (Mike_Fontenot) responded:
> No, Greek indices are reserved for COEFFICIENTS
> in Wald's notation.
I should have added that Wald also uses Greek indices for basis vectors
and basis duals. So he uses a DIFFERENT notation for basis vectors than
for other vectors (and likewise for basis duals versus other duals).
That's one of the things I dislike about Wald's notation. I've designed
my notation so that basis vectors are treated the same as other vectors
(and likewise for basis duals and other duals).
I also dislike the fact that Wald uses the SAME root-letter to represent
basis duals and basis vectors (a lower-case "e"). But the basis dual
corresponding to a given basis vector (via the "delta" relationship) is
NOT the dual which is "metric-isomorphic" to that vector. And
elsewhere, Wald uses (as I do) the same root-letter to represent duals
and vectors which ARE "metric-isomorphic". I think he is being
inconsistent there. I use a DIFFERENT root-letter (D) for basis duals
than for basis vectors (E), to make clear that they are NOT
metric-isomorphic.
Mike Fontenot
when saving it from my inbox into my s.p.r articles-to-be-moderated queue.
I apologise to the author and other readers for this, and for the ensuing
loss of threading in many newsreaders.
-- jt]]
Theo Wollenleben wrote:
>
> [...]
>
>
And I (Mike_Fontenot) responded:
> No, Greek indices are reserved for COEFFICIENTS
> in Wald's notation.
I should have added that Wald also uses Greek indices for basis vectors
and basis duals. So he uses a DIFFERENT notation for basis vectors than
for other vectors (and likewise for basis duals versus other duals).
That's one of the things I dislike about Wald's notation. I've designed
my notation so that basis vectors are treated the same as other vectors
(and likewise for basis duals and other duals).
I also dislike the fact that Wald uses the SAME root-letter to represent
basis duals and basis vectors (a lower-case "e"). But the basis dual
corresponding to a given basis vector (via the "delta" relationship) is
NOT the dual which is "metric-isomorphic" to that vector. And
elsewhere, Wald uses (as I do) the same root-letter to represent duals
and vectors which ARE "metric-isomorphic". I think he is being
inconsistent there. I use a DIFFERENT root-letter (D) for basis duals
than for basis vectors (E), to make clear that they are NOT
metric-isomorphic.
Mike Fontenot