Global Barbero-Immirzi Connections - General Relativity and Quantum CosmologyReport as inadecuate

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Abstract: The Barbero-Immirzi BI connection, as usually introduced out of a spinconnection, is a global object though it does not transform properly as agenuine connection with respect to generic spin transformations, unless quitespecific and suitable gauges are imposed. We shall here investigate whether andunder which global conditions a properly transforming and hence globalSU2-connection can be canonically defined in a gauge covariant way in such away that SU2-connection locally agrees with the usual BI connection and canbe defined on pretty general bundles in particular triviality is not assumed.As a by-product we shall also introduce a global covariant SU2-connectionover the whole spacetime while for technical reasons the BI connection in thestandard formulation is just introduced on a space slice which restricts tothe usual BI connection on a space slice.

Author: L.Fatibene, M.Francaviglia


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