Gamma-Traceless condition

[Maria Isabel Iguti]

Hi everyone, I’m trying to implement Gamma-traceless condition (spinor tensor) on Xact, the program understands the condition, but in other expressions he don’t implement this condition. Someone can help me, please.

The condition is writen as: 

\[Psi] /: Gammagg[\[Mu]_, B_, A_]\[CenterDot]\[Psi][\[Nu]_, -A_] /;
  PairQ[\[Mu], \[Nu]] := 0

[Thomas Bäckdahl]

Hi!

Can you provide a notebook with a smallest non-working example?
With that it is much easier to track down the problem.

Regards
Thomas

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[Markus B. Fröb]

Dear Maria,

it seems that you are using FieldsX. In this case, please try

\[Psi] /: Gammagg1[\[Mu]_, B_, A_]\[CenterDot]\[Psi][\[Nu]_, -A_] /;

PairQ[\[Mu], \[Nu]] := 0

In patterns, one has to specify the number of indices that the gamma
matrices have, since these are the actual tensors defined by FieldsX.
Gammagg itself is only a function that returns the right tensor.

Best, Markus


Zitat von Maria Isabel Iguti <m.i...@unesp.br>:

[Markus B. Fröb]

Dear Maria,

I'm not sure what you mean by "don't work".

In your notebook, I see that the terms eq1 and eq3 are simplified to
zero as by the rule.
This looks to me working correctly.

If there is something else that does not work, please send a minimal
working example (MWE) that shows exactly what you think is incorrect,
and what you believe it should be. Without any explanation, or with
long additional extra code and output, it is very difficult to
understand what is going on.

Some things that I noticed when looking at the notebook:
- in your definition of L there is a non-commutative product missing
between Gamma3 and PD of psi, also in the definition of theta between
the RightVarD and the PD psi
- when you define rules which involve patterns, like theta[mu_,nu_] or
K1G[rho_,mu_,nu_], you need to use := instead of =
(see for example the Mathematica documentation:
https://reference.wolfram.com/language/tutorial/FunctionsAndPrograms.html#13037)

Best, Markus


Zitat von Maria Isabel Iguti <m.i...@unesp.br>:

> Hi, I try to use

> \[Psi] /: Gammagg1[\[Mu]_, B_, A_]\[CenterDot]\[Psi][\[Nu]_, -A_] /;
> PairQ[\[Mu], \[Nu]] := 0
>

> but don't work, this is my notebook
>
>
>
> Em sex., 9 de ago. de 2024 às 07:33, Markus B. Fröb <
> mfr...@itp.uni-leipzig.de> escreveu:

[Maria Isabel Iguti]

Hi, I try to use 

\[Psi] /: Gammagg1[\[Mu]_, B_, A_]\[CenterDot]\[Psi][\[Nu]_, -A_] /; 
PairQ[\[Mu], \[Nu]] := 0

but don't work, this is my notebook

Em sex., 9 de ago. de 2024 às 07:33, Markus B. Fröb <mfr...@itp.uni-leipzig.de> escreveu: