- #1
Claret
- 1
- 0
I am struggleing in an identity, i.e. [tex]\nabla_m R_{ikjl}(\overline{\epsilon}\psi^m)(\overline{\psi^i}\psi^j)(\overline{\psi^k}\psi^l)=0[/tex] ,
where [tex]i,j,k,l,m[/tex] are dummy indices, [tex]\nabla_m[/tex] is covariant derivative, [tex]R_{ikjl}[/tex] is Riemann-Christoffel curvature tensor, and it is known that, for any two arbitary spinors [tex]\psi^i,\psi^j[/tex], [tex]\overline{\psi^i}\psi^j=\overline{\psi^j}\psi^i[/tex].
I think one could use Bianchi Identity to prove this, but I failed...who can do me a favor? Thanks!
where [tex]i,j,k,l,m[/tex] are dummy indices, [tex]\nabla_m[/tex] is covariant derivative, [tex]R_{ikjl}[/tex] is Riemann-Christoffel curvature tensor, and it is known that, for any two arbitary spinors [tex]\psi^i,\psi^j[/tex], [tex]\overline{\psi^i}\psi^j=\overline{\psi^j}\psi^i[/tex].
I think one could use Bianchi Identity to prove this, but I failed...who can do me a favor? Thanks!