Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 38, Issue 14, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6382/ac011b
Keywords
quantum gravity; spin foam dynamics; effective spin foams; area spectrum; flatness problem; second class constraints; loop quantum gravity
Categories
Funding
- Perimeter Institute for Theoretical Physics
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Colleges and Universities
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This study presents the first computation of spin foam dynamics that acts as a test of the quantum equations of motion of gravity. The results reveal a rich semiclassical regime, but emphasize the need to understand the interplay between various parameters. Additionally, the subtle nature of the semiclassical regime is shown to be a generic feature of path integral quantization of systems with second class constraints.
The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently introduced effective spin foam models, which are particularly numerically efficient. Previous work has raised the concern of a flatness problem in spin foam dynamics, identifying the potential for the dynamics to lead to flat geometries in the small PLANCK CONSTANT OVER TWO PI semiclassical limit. The numerical results presented here expose a rich semiclassical regime, but one that must be understood as an interplay between the various parameters of the spin foam model. In particular, the scale of the triangulation, fixed by the areas of its boundary triangles, the discreteness of the area spectrum, input from loop quantum gravity, and the curvature scales around the bulk triangles, all enter the characterization of the semiclassical regime identified here. In addition to these results on the dynamics, we show that the subtle nature of the semiclassical regime is a generic feature of the path integral quantization of systems with second class constraints.
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