Ntina Savvidou 2006 Class. Quantum Grav. 23 4133 doi:10.1088/0264-9381/23/12/010
Ntina Savvidou
Show affiliationsWe 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 3-surface and it does not have a natural spacetime interpretation, this does not mean that the Barbero connection is not a suitable variable for quantization; it appears naturally in the formalism even in the 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.
04.20.Cv Fundamental problems and general formalism
04.20.Fy Canonical formalism, Lagrangians, and variational principles
04.20.Gz Spacetime topology, causal structure, spinor structure
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
83C75 Space-time singularities, cosmic censorship, etc.
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds (See also 22E65, 57S05)
Issue 12 (21 June 2006)
Received 7 February 2006
Published 26 May 2006
Ntina Savvidou 2006 Class. Quantum Grav. 23 4133
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