Geodesic round trips by parallel transport in quantum gravity

Details Geodesic round trips by parallel transport in quantum gravity Geodesic round trips by parallel transport in quantum gravity

Jan 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phrvd..47..502m&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 47, Issue 2, 15 January 1993, pp.502-509

Physics

14

Theory Of Quantized Fields, Fundamental Problems And General Formalism

Scientific paper

We study the vacuum correlations of a gravitational field in any dimension N>2 using the perturbative expansion to order G. It is known that the usual Green's functions are meaningless in quantum gravity; moreover, we show that the traces of the holonomies of the Christoffel connection vanish, revealing a striking difference between gravity and Yang-Mills theories. In order to define meaningful holonomies we make two physical requirements: (1) the contours of the loop integrals must have ``geodesic form and size'' (2) the full rotation matrices, not just their traces, must be averaged. Following these ideas we compute a ``dumbbell correlation function'' which turns out to behave like G/DN+2, where D is the geodesic distance. Finally, we write a gauge-invariant quantity which could replace the Wilson loop in reproducing the static potential energy between two sources.

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