Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product

TL;DR

This paper investigates the invariance properties of the gravity path-integral measure within the canonical framework and explores how to construct a spin-foam model that serves as a physical inner product.

Contribution

It extends previous work by analyzing gauge invariance of the path-integral measure and proposing a suitable formula for spin-foam models as a canonical inner product.

Findings

Identifies gauge invariance properties of the path-integral measure.

Proposes a concrete path-integral formula for spin-foam models.

Links the path-integral measure to the physical inner product in canonical gravity.

Abstract

This article serves as a continuation for the discussion in arXiv:0911.3433, we analyze the invariance properties of the gravity path-integral measure derived from canonical framework, and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory.