Dérivations, formes et opérateurs usuels sur les champs spinoriels des variétés différentiables de dimension paire
Differential forms as spinors
Do Barbero-Immirzi connections exist in different dimensions and signatures?
We shall show that no reductive splitting of the spin group exists in dimension other than in dimension . In dimension there are reductive splittings in any signature. Euclidean and Lorentzian signatures are reviewed in particular and signature is investigated explicitly in detail. Reductive splittings allow to define a global -connection over spacetime which encodes in an weird way the holonomy of the standard spin connection. The standard Barbero-Immirzi (BI) connection used in LQG is...