Abstract
Clifford algebras and Majorana conditions are analyzed in any space–time. An index labelling inequivalent Γ-structures up to orthogonal conjugations is introduced. Inequivalent charge-operators in even dimensions, invariant under Wick rotations, are considered. The hermiticity condition on free-spinors Lagrangians is presented. The constraints put by the Majorana condition on the free-spinors dynamics are analyzed. Tables specifying which space–times admit Lagrangians with nonvanishing kinetic, massive or pseudo-massive terms (for both charge-operators in even dimensions) are given. The admissible free Lagrangians for free Majorana–Weyl spinors are fully classified.
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