Observers, observables, spinors, and the confusion of tongues

Choquet-Bruhat was the first to give a proper physical definition of covariant spinors, taking into account the reference system and treating them as equivalence classes defined from the transformation laws of the representatives when the reference system is changed. Recently, Rodriguez et al. [ Int. J. Theor. Phys. 35, 1849 (1996)] have adapted this procedure from covariant spinors to the case of algebraic and operator spinors. These approaches are restrained in the sense that the type of spinor is chosen from the beginning, and it does not admit a general formulation. In this paper, we present a unified definition that is valid for any type of the space of representation, being independent of its particular properties. In our formulation the three types of spinors appear as particular cases of the general definition. Moreover, we stick out the importance of the bilinear covariants in the definition of spinors. From this, we recognize a completely different kind of spinor, characterized by the different nature of their bilinears. The unnoticed difference between this last one, which we have called right-operator spinors, and the previous (left-)operator spinors has been motive of a long time discussion.