Real Structures in Clifford Algebras and Majorana Conditions in Any Space-time

Details Real Structures in Clifford Algebras and Majorana Conditions in Any Space-time Real Structures in Clifford Algebras and Majorana Conditions in Any Space-time

1999-04-20

arxiv.org/abs/hep-th/9904134v2

Mod.Phys.Lett. A14 (1999) 1797-1814

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LaTex. Some remarks added

Scientific paper

10.1142/S0217732399001899

Clifford algebras and Majorana conditions are analyzed in any spacetime. An index labeling 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 spacetimes admit lagrangians with non-vanishing kinetic, massive or pseudomassive 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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