Absence of Differential Correlations Between the Wave Equations for Upper-Lower One-Index Twistor Fields Borne by the Infeld-van der Waerden Spinor Formalisms for General Relativity

Abstract

It is pointed out that the wave equations for any upper-lower one-index twistor fields which take place in the frameworks of the Infeld-van der Waerden {\gamma}{\epsilon}-formalisms must be formally the same. The only reason for the occurrence of this result seems to be directly related to the fact that the spinor translation of the traditional conformal Killing equation yields twistor equations of the same form. It thus appears that the conventional torsionless devices for keeping track in the {\gamma}-formalism of valences of spinor differential configurations turn out not to be useful for sorting out the typical patterns of the equations at issue.