[GiNaC-list] question about lorentz_g contract with sy_anti tensor

Vladimir V. Kisil kisilv at maths.leeds.ac.uk
Thu May 23 11:45:50 CEST 2019

>>>>> On Thu, 23 May 2019 00:57:21 +0000, Feng Feng <F.Feng at outlook.com> said:

    FF> Hi all, I wonder is there a way or method to simplify the
    FF> expression with a sy_anti tensor contracted with a lorent_g to
    FF> 0?

    You will get 0 if you will use
    auto ret = indexed(A, sy_anti(0,1,2,3), ia,ib,ic,id) * lorentz_g(ic, id.toggle_variance());

    Anti-symmetry is not applied to varidx with different variance.
Vladimir V. Kisil                 http://www.maths.leeds.ac.uk/~kisilv/
  Book:     Geometry of Mobius Transformations     http://goo.gl/EaG2Vu
  Software: Geometry of cycles          http://moebinv.sourceforge.net/

    FF> Please have a look at the following code, I expect ret is 0, and
    FF> the output looks like “A~b~a.c~c”, it is actually

    FF> 0 due to the sy_anti, but I wonder, is there a way or a method
    FF> to simplify those expression directly to 0?

    FF> Thanks very much!

    FF> using namespace GiNaC;

    FF> using namespace std;

    FF> int main(int argc, char** argv) {

    FF>     symbol a("a"), b("b"), c("c"), d("d"), A("A");

    FF>     symbol D("D");

    FF>     varidx ia(a,D), ib(b,D), ic(c,D), id(d,D);

    FF>     auto ret = indexed(A, sy_anti(0,1,2,3), ia,ib,ic,id) *
    FF> lorentz_g(ic.toggle_variance(), id.toggle_variance());

    FF>     cout << simplify_indexed(ret) << endl;

    FF>     return 0;

    FF> }

    FF> Best regards!

    FF> Feng

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