Some Considerations on Discrete Quantum Gravity

TL;DR

This paper explores the relationship between Local Regge Calculus and Spin Foam Formalism, demonstrating how Barrett-Crane Quantization bridges the two and deriving inter-twiner terms from closure constraints.

Contribution

It introduces Barrett-Crane Quantization into Local Regge Calculus, establishing a connection with Spin Foam Formalism and deriving key structural terms.

Findings

Unique spin assignment to hinges via Barrett-Crane Quantization

Inter-twiner terms derived from closure constraints

Bridging Local Regge Calculus with Spin Foam Formalism

Abstract

Recent results in Local Regge Calculus are confronted with Spin Foam Formalism. Introducing Barrett-Crane Quantization in Local Regge Calculus makes it possible to associate a unique Spin $j_{h}$ with an hinge $h$, fulfilling one of the requirements of Spin Foam definition. It is shown that inter-twiner terms of Spin Foam can follow from the closure constraint in Local Regge Calculus. Dedicated to Beppe Marmo for his 65th Birthday