Why "SameDummies" does not work in this case?

[Behnoush Khavari]

Hi,

As I have written in the attached file, the command "SameDummies" does not help to simplify, say an expression like 

n[-b] T[a,b,d,-d]+n[-d] T[a,d,b,-b].  I was wondering if I need to add something to this command or whether there is any other command doing this. As a matter of fact, I am trying to avoid the command " ToCanonical", since it reorders indices in a way which is not so convenient for my case.

Thank you,

Behnoush

[Thomas Bäckdahl]

Hi!

SameDummies is not supposed to canonicalize the dummy indices. It is just there to make sure that the same set of indices are used as dummies in all terms. Your first example would not have worked if you change c to f.

I believe that the right tool here should be ToCanonical. Can you tell us why the index ordering of ToCanonical is inconvenient for you? Perhaps we can find a way around that.

Regards
Thomas

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[Behnoush Khavari]

Hi Thomas,

Thank you for your reply.

Actually, because as far as I see, ToCaninical also contracts indices when the metric is also present in the expression.

However, in my calculation and at the stage that I want to do this reordering of dummy indices, this contraction should not be done. 

The reason is that, I am dealing with a 4d manifold splitted to 3 submanifols and want to write a quantity defined in the 4d manifold in terms of some tensors defined in its submanifolds.

Since at the current stage of calculation,  the metric is yet that of 4d manifold, while the indices are now the ones related to each of the 3 submanifolds (Because I have already applied the command TraceProductDummy),  using ContractMetric at this stage would not give a correct result.

 I know that I can use it after that I state the hole metric in terms of metrics of submanifolds , but I am trying to simplify the expression as far as it is possible at this very stage to avoid getting very long expressions in the middle parts of calculation.

.

That's why I needed a command for only renaming dummy indices.

I hope my explanation of the problem is clear now.

Thank you again.

Behnoush 

[Behnoush Khavari]

در سه‌شنبه 21 ژوئن 2016، ساعت 19:08:10 (UTC+4:30)، TB نوشته:

[Thomas Bäckdahl]

Hi!

One can tell ToCanonical that it should not use the metric globally with
SetOptions[ToCanonical, UseMetricOnVBundle -> None];

or locally like this
ToCanonical[%, UseMetricOnVBundle -> None]

I hope this helps. Just be careful with 1D submanifolds -- there is a recent thread about that case.

Regards
Thomas

[Behnoush Khavari]

Hi,

Yes, I am actually already using // ToCanonical[#, UseMetricOnVBundle -> None] &, and it still contracts indices.

Maybe because, as I told, the metric symbol is still that of the 4d manifold, while its indices are those related to the 3 different submanifolds. So, the problem is still there.

Thank you for the warning, I guess you mean my own recent post on the problem with the wrong mixing of indices of partial derivatives. 

That's already been solved by the very helpful solution you suggested.

Best regards,

Behnoush

در سه‌شنبه 21 ژوئن 2016، ساعت 22:42:59 (UTC+4:30)، TB نوشته: