[GiNaC-list] dirac_slash(0) Does'nt work !!!

[Sheplyakov Alexei]

Hello!

On Fri, Aug 03, 2007 at 11:22:56AM -0700, J. gallardo wrote:
> 
> I'm trying to write an expression wich uses a Dirac " gamma 0 " for
> calculations on spin polarization projector, the line looks like:
> 
> ex XAA=dirac_slash(0)* dirac_slash(k,4)*proj1* dirac_slash(E,4)*
> (dirac_slash(p,4)+ m * dirac_ONE()) * dirac_slash(E,4) *
> dirac_slash(k,4)*proj1* dirac_slash(E1,4) * (dirac_slash(p1,4)+m *
> dirac_ONE());

Write your expression in Lorentz-invariant way:

 ex XAA=dirac_slash(P0, 4)*dirac_slash(k,4)*proj1* dirac_slash(E,4)*
 (dirac_slash(p,4)+ m*dirac_ONE())*dirac_slash(E,4)*
 dirac_slash(k,4)*proj1*dirac_slash(E1,4)*(dirac_slash(p1,4)+m*dirac_ONE());

 ex result = dirac_trace(XAA).expand(expand_options::expand_indexed); 
 // or whatever

And calculate invariant combinations in whatever reference frame:

 scalar_products sp;
 symbol k0("k0"), E10("E10), p10("p10"), E0("E0");
 sp.add(P0, k, k0);
 sp.add(P0, p, p0);
 sp.add(P0, E1, E10);
 sp.add(P0, E, E0);
 // add something for p*k and so on...

 result = result.simplify_indexed(sp);

Another possible variant is (I don't recommend it):

 varidx mu(symbol(mu), 4);
 ex XAA=dirac_gamma(mu)*dirac_slash(k,4)*proj1* dirac_slash(E,4)*
 (dirac_slash(p,4)+ m*dirac_ONE())*dirac_slash(E,4)*
 dirac_slash(k,4)*proj1*dirac_slash(E1,4)*(dirac_slash(p1,4)+m*dirac_ONE());
 XAA = XAA.subs(mu==0);


Best regards,
 Alexei


-- 
All science is either physics or stamp collecting.

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