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On a Covariant Formulation of the Barbero-Immirzi Connection

L. Fatibene·M. Francaviglia·C. Rovelli
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Abstract

The Barbero-Immirzi (BI) connection, as usually introduced out of a spin connection, is a global object though it does not transform properly as a genuine connection with respect to generic spin transformations, unless quite specific and suitable gauges are imposed. We shall here investigate whether and under which global conditions a (properly transforming and hence global) SU(2)-connection can be canonically defined in a gauge covariant way. Such SU(2)-connection locally agrees with the usual BI connection and it can be defined on pretty general bundles; in particular triviality is not assumed. As a by-product we shall also introduce a global covariant SU(2)-connection over the whole spacetime (while for technical reasons the BI connection in the standard formulation is just introduced on a space slice) which restricts to the usual BI connection on a space slice.

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L. Fatibene, M. Francaviglia, C. Rovelli. 2007-02-26. On a Covariant Formulation of the Barbero-Immirzi Connection. https://doi.org/10.1088/0264-9381%2F24%2F11%2F017

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