A twistorial description of the dynamics of complexified Dirac fields

A method that allows the construction of a twistorial least-action principle for complexified Klein-Gordon fields is adapted to the context of the two-component theory of Dirac fields. It appears that the viability of the adaptation procedures rests crucially upon the freedom in the selection of spinor kernels for the integrands of the universal twistor contour integrals for massive fields carrying arbitrary spin. An intrinsic ambiguity borne by the inner structure of the twistor representation of the dynamics of the spinning fields taken into consideration is then brought out. This feature appears to be reflected by the fact that many Poincare-invariant Lagrangian densities can be regarded as candidates for entering the new variational principle. It is remarked that all the corresponding equations of motion agree with a single twistor translation of the pertinent field equations. The dynamical expressions that result from the implementation of the procedures turn out to be related to one another through a simple interchange scheme. A set of wave equations for the system allowed for is also obtained. (author)