Spin Foam Quantization and Anomalies

TL;DR

This paper investigates the derivation of spin foam amplitudes from the path integral measure, emphasizing the importance of anomaly-free measures and background independence for consistent quantum gravity models.

Contribution

It establishes a connection between spin foam amplitudes and the path integral measure, proposing a simple anomaly-free model consistent with background independence.

Findings

Derived spin foam amplitudes from the path integral measure.

Identified restrictions for anomaly-free measures based on background independence.

Presented a new spin foam model related to the Husain--Kuchar model.

Abstract

The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their large-spin behavior determines the convergence properties of the state-sum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the Husain--Kuchar model.