[GiNaC-devel] Improved dummy index renaming -> clifford exam fails

[Chris Dams]

Dear Vladimir,

On Mon, 14 Aug 2006, Vladimir Kisil wrote:

>     CD> the metric with up-indices is the inverse of the metric with
>     CD> down-indices, we arive at the identity
>     CD> e~mu e~alpha e.mu = (2 - dim) * e~alpha,
>     CD> where dim is the number of row/columns of the metric.
> 
> 	I saw this rule in the diracgamma contraction but have doubts that it
>   will be simple as that for generic Clifford units with metric
>   diag_matrix(1,-1,0) for example. 

Let us take that to be the metric for down-indices for definiteness. Now
we are going to run into trouble if we ask what the result is if it is
given up-indices. That should be the inverse... not such a good idea.  
Furthermore, from e.mu = g.mu.nu e~nu it follows that e.3 = 0, no matter
what the e~mu are (it is actually rather unclear what e~3 would/should be
in this case).

Maybe it just wasn't your intention to take varidxes to mean the same as
is common among physicists. This is why I also mentioned the possibility
that clifford objects with a matrix as metric should take normal idxes
instead of varidxes. Or even the possibility that matrices should only
take normal indices and not varidxes.

Best wishes,
Chris