- #1
earth2
- 86
- 0
Hey guys,
I have a question about said spinors.
In supersymmetry introductions one finds (e.g. for two left-handed spinors [tex] \eta [/tex], [tex] \nu [/tex]) that [tex]\eta\nu=\nu\eta[/tex] due to their Grassmannian character and the antisymmetry of the spinor product.
If I look, however, at modern field theoretical methods that rely on the fact that SO(3,1) is doubly covered by SL(2,C) to express 4-vectors in terms of Weyl spinors, I find for the spinor product of two left-handed Weyl spinors (in a slightly different notation) [tex]\langle \nu |[/tex], [tex]\langle \eta |[/tex] is given by
[tex]\langle \nu |\eta\rangle=-\langle \eta |\nu\rangle[/tex].
I don't see where the minus-sign enters, since in my view only the notation is different, whereas the definition of the spinor product is the same in the two cases...
Does someone know where the difference comes from?
Cheers,
earth2
I have a question about said spinors.
In supersymmetry introductions one finds (e.g. for two left-handed spinors [tex] \eta [/tex], [tex] \nu [/tex]) that [tex]\eta\nu=\nu\eta[/tex] due to their Grassmannian character and the antisymmetry of the spinor product.
If I look, however, at modern field theoretical methods that rely on the fact that SO(3,1) is doubly covered by SL(2,C) to express 4-vectors in terms of Weyl spinors, I find for the spinor product of two left-handed Weyl spinors (in a slightly different notation) [tex]\langle \nu |[/tex], [tex]\langle \eta |[/tex] is given by
[tex]\langle \nu |\eta\rangle=-\langle \eta |\nu\rangle[/tex].
I don't see where the minus-sign enters, since in my view only the notation is different, whereas the definition of the spinor product is the same in the two cases...
Does someone know where the difference comes from?
Cheers,
earth2