[GiNaC-list] dirac_spinor?

[Vladyslav Shtabovenko]

Dear Vladimir,

 >    However, if this is still not sufficient you may derive something
 >    from clifford class adding something more involved than int
 >    for the commutator_sign.

thanks, this makes sense.

I guess this is what one has to do at the end if one wants to implement
new things in the handling of Dirac algebra. Apart from spinors, one 
could also add a non-naive renormalization scheme for Dirac gamma^5, 
where the anitcommutator of {g^5,g^mu} is non-zero in D-dimensions.

However, this would be a rather formidable undertaking ...

Cheers,
Vladyslav




On 27/08/14 18:53, Vladimir V. Kisil wrote:
> 	Dear Vladislav,
>>>>>> On Wed, 27 Aug 2014 17:12:23 +0200, Vladyslav Shtabovenko <v.shtabovenko at tum.de> said:
>      VSh> However, this doesn't seem to be possible since the eval_ncmul
>
>      That is true, if you are going to use precooked Dirac
>    gammas. However, the clifford class has the member
>
> int commutator_sign; /**< It is the sign in the definition e~i e~j +/- e~j e~i = B(i, j) + B(j, i)*/
>
>    This allows to implement either commuting rules or anti-commuting
>    rules for a particular clifford object. In particular, some while
>    ago I have experimented with a Lie algebra implementation as a
>    clifford object of GiNaC (the code is available on request). Also,
>    clifford objects with different representation labels simply
>    commute. This combination gives a significant freedom for implementing
>    various algebraic rules.
>
>    However, if this is still not sufficient you may derive something
>    from clifford class adding something more involved than int
>    for the commutator_sign.
>
>    Best wishes,
>    Vladimir
>