Wilson loops in four-dimensional quantum gravity
- Center for Theoretical Physics, Laboratory for Nuclear Science, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139 (United States)
A Wilson loop is defined, in four-dimensional pure Einstein gravity, as the trace of the holonomy of the Christoffel connection or of the spin connection, and its invariance under the symmetry transformations of the action is shown (diffeomorphisms and local Lorentz transformations). We then compute the loop perturbatively, both on a flat background and in the presence of an external source; we also allow some modifications in the form of the action, and test the action of stabilized'' gravity. A geometrical analysis of the results in terms of the gauge group of the Euclidean theory, SO(4), leads us to the conclusion that the corresponding statistical system does not develop any configuration with localized curvature at low temperature. This nonlocal'' behavior of the quantized gravitational field strongly contrasts with that of usual gauge fields. Our results also provide an explanation for the absence of any invariant correlation of the curvature in the same approximation.
- DOE Contract Number:
- AC02-76ER03069
- OSTI ID:
- 7116954
- Journal Information:
- Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:12; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
INVARIANCE PRINCIPLES
LIE GROUPS
LORENTZ TRANSFORMATIONS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
SO GROUPS
SO-4 GROUPS
SYMMETRY
SYMMETRY GROUPS
TRANSFORMATIONS
WILSON LOOP