We investigate to what extent a spinor is recovered from $S$, $P$, $V_{\mu }$, $A_{\mu }$, and $T_{\mu \nu }$ 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.

• Received 25 May 1982

DOI:https://doi.org/10.1103/PhysRevD.26.2169