Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-02-07
Class.Quant.Grav. 23 (2006) 4133-4150
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages
Scientific paper
We present a histories version of the connection formalism of general relativity. Such an approach introduces a spacetime description--a characteristic feature of the histories approach--and we discuss the extent to which the usual loop variables are compatible with a spacetime description. In particular, we discuss the definability of the Barbero connection without any gauge fixing. Although it is not the pullback of a spacetime connection onto the three-surface and it does not have a natural spacetime interpretation, this does not mean that the Barbero connection is not suitable variable for quantisation; it appears naturally in the formalism even in absence of gauge fixing. It may be employed therefore, to define loop variables similar to those employed in loop quantum gravity. However, the loop algebra would have to be augmented by the introduction of additional variables.
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