A spin-foam vertex amplitude with the correct semiclassical limit

TL;DR

This paper modifies the EPRL spin-foam amplitude to isolate a single gravitational sector, ensuring the correct semiclassical limit for loop quantum gravity, addressing issues caused by multiple sectors in the original formulation.

Contribution

It introduces a modification to the EPRL spin-foam amplitude that isolates a single gravitational sector, achieving the correct semiclassical behavior.

Findings

Modified amplitude yields the correct semiclassical limit

Identifies the cause of extra terms in the original amplitude

Provides a more consistent spin-foam model for loop quantum gravity

Abstract

Spin-foam models are hoped to provide a dynamics for loop quantum gravity. These start from the Plebanski formulation of gravity, in which gravity is obtained from a topological field theory, BF theory, through constraints, which, however, select more than one gravitational sector, as well as an unphysical degenerate sector. We show this is why terms beyond the needed Feynman-prescribed one appear in the semiclassical limit of the EPRL spin-foam amplitude. By quantum mechanically isolating a single gravitational sector, we modify this amplitude, yielding a spin-foam amplitude for loop quantum gravity with the correct semiclassical limit.