Supergravity, supersymmetry: A geometric unitary spinor theory.

*(English)*Zbl 0789.53051
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 177-199 (1992).

As it is well known, supersymmetry and supergravity were intensively studied by using an anticommutative analysis on superspaces and supermanifolds. The author shows in the present paper that it is possible to avoid such complicated machinery by considering spinors as elements of minimal left ideals in a Clifford algebra. By this method, supersymmetries appear naturally for tensor-spinor fields, connected with Bianchi identities and Einstein-Hilbert equations. The method is first developed on the usual curved space-time and then it is extended to the construction of \(N\)-supergravitation theories \((N = 2^ k)\).

For the entire collection see [Zbl 0764.00002].

For the entire collection see [Zbl 0764.00002].

Reviewer: A.Bejancu (Iaşi)

##### Keywords:

superspaces; Clifford algebra; tensor-spinor fields; Bianchi identities; Einstein-Hilbert equations
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\textit{A. Crumeyrolle}, in: Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North-Holland Publishing Company; Budapest: János Bolyai Mathematical Society. 177--199 (1992; Zbl 0789.53051)