On the consistency of the constraint algebra in spin network quantum gravity

TL;DR

This paper examines the properties of Thiemann's quantum Hamiltonian constraints in Euclidean gravity, focusing on the algebra of constraints and the quantum realization of specific classical objects.

Contribution

It analyzes the constraint algebra and the quantum representation of the classical Poisson bracket related to the Hamiltonian constraints.

Findings

Identifies features of Thiemann's quantum Hamiltonian constraints.

Discusses the quantum realization of $q^{ab}V_b$ as a Poisson bracket.

Highlights issues in the constraint algebra in quantum gravity.

Abstract

We point out several features of the quantum Hamiltonian constraints recently introduced by Thiemann for Euclidean gravity. In particular we discuss the issue of the constraint algebra and of the quantum realization of the object $q^{ab}V_b$, which is classically the Poisson Bracket of two Hamiltonians.