Evaluation of new spin foam vertex amplitudes

TL;DR

This paper extends an algorithm to evaluate new spin foam vertex amplitudes, compares different models using a unified approach, and analyzes their semiclassical behavior and asymptotics, revealing non-oscillatory decay and limitations in semiclassical wave packet propagation.

Contribution

It introduces a generalized algorithm for evaluating new spin foam models and provides a systematic comparison and analysis of their semiclassical properties.

Findings

New models show non-oscillatory, power-law decay similar to Barrett-Crane.

Semiclassical wave packet analysis indicates models may not behave semiclassically for generic states.

A unified methodology for comparing spin foam models is proposed.

Abstract

The Christensen-Egan algorithm is extended and generalized to efficiently evaluate new spin foam vertex amplitudes proposed by Engle, Pereira & Rovelli and Freidel & Krasnov, with or without (factored) boundary states. A concrete pragmatic proposal is made for comparing the different models using uniform methodologies, applicable to the behavior of large spin asymptotics and of expectation values of specific semiclassical observables. The asymptotics of the new models exhibit non-oscillatory, power-law decay similar to that of the Barrett-Crane model, though with different exponents. Also, an analysis of the semiclassical wave packet propagation problem indicates that the Magliaro, Rovelli and Perini's conjecture of good semiclassical behavior of the new models does not hold for generic factored states, which neglect spin-spin correlations.