Curvature in spinfoams

[Philip Thrift]

https://arxiv.org/pdf/1103.4602.pdf

Curvature in spinfoams

Elena Magliaro and Claudio Perini

Institute for Gravitation and the Cosmos, Physics Department,

Penn State, University Park, PA 16802-6300, USA

(Dated: June 10, 2018)

We consider spinfoam quantum gravity. We show in a simple case that the amplitude projects over a nontrivial (curved) classical geometry. This suggests that, at least for spinfoams without bubbles and for large values of the boundary spins, the amplitude takes the form of a path integral over Regge metrics, thus enforcing discrete Einstein equations in the classical limit. The result relies crucially on a new interpretation of the semiclassical limit for the amplitudes truncated to a fixed 2-complex.

The physical picture emerging from the spinfoam gravity is that of a discrete, combinatorial spacetime structure (a quantum foam of virtual geometries), where the Plank scale plays the role of a

natural minimal length. Spinfoams are the result of the quantization of general relativity formulated as a constrained BF theory. 

@philipthrift

[Lawrence Crowell]

It looks an awful lot like spinorial Regge calculus. The real issue though is topology more than curvature. How is it that topological indices, which are quantum numbers, exist in some indexed set of eigenvalues, when their constancy requires there to be some sort of conserved quantum number. In other words, the evolution of the "foam" or quantum superposed spatial surfaces change these topological indices as eigenvalues that can change their relative amplitudes.

LC