Real structures in Clifford algebras and Majorana conditions in any space-time

摘要

Clifford algebras and Majorana conditions are analyzed in any space-time. An index labelling inequivalent #GAMMA#-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.