Graviton propagator in loop quantum gravity

TL;DR

This work develops a boundary--amplitude approach within loop quantum gravity to compute covariant graviton propagators in a background--independent setting. By formulating a generally covariant two--point function from boundary data and employing spinfoam dynamics in the GFT/B model, the authors show that the first two orders in the coupling expansion $\\lambda$ reproduce the linearized gravity propagator at large distances, with exact $1/|x-y|^2$ scaling. The analysis hinges on a Gaussian boundary state peaked on both intrinsic and extrinsic boundary geometry and on carefully handling the asymptotics of the Barrett–Crane 10$j$ symbol to suppress unwanted degenerate contributions. The results demonstrate the viability of computing particle--like correlators in a fully background--independent quantum gravity and lay the groundwork for higher--order and non--diagonal components. This framework provides a concrete route to connecting nonperturbative quantum gravity to low--energy gravitational physics and Newtonian limits.

Abstract

We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.

Figures (6)

• Figure 1: The boundary graph $\Gamma$ and the boundary spin network $s$.
• Figure 2: The spacetime triangulation $\Delta$ together with its 3d and 2d analogs.
• Figure 3: The spacetime triangulation.
• Figure 4: Decomposition
• Figure 5: On the left, the triangulated spacetime. On, the right, its dual drawn around the Feynman graph.