Global Barbero-Immirzi Connections

Details Global Barbero-Immirzi Connections Global Barbero-Immirzi Connections

2009-05-13

arxiv.org/abs/0905.2031v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

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 in such a way that SU(2)-connection locally agrees with the usual BI connection and 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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