Reconstruction of a spinor via Fierz identities
Yasushi Takahashi · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1982
We investigate to what extent a spinor is recovered from $S$, $P$, ${V}_{\ensuremath{\mu}}$, ${A}_{\ensuremath{\mu}}$, and ${T}_{\ensuremath{\mu}\ensuremath{ u}}$ satisfying the Fierz identities. To do this, we introduce a parameter representation for the 16 tensor quantities, which takes care of all the Fierz identities, and set up a spinor-determining equation. This equation is solved. The solution contains 4 arbitrary complex numbers. These constants can be determined except an overall phase if we demand that the bilinear forms agree with the original 16 tensor quantities.