New Hamiltonian constraint operator for loop quantum gravity

TL;DR

This paper introduces a new symmetric Hamiltonian constraint operator for loop quantum gravity that is well-defined, anomaly-free, and applicable to cosmological models, improving upon previous methods.

Contribution

A novel symmetric Hamiltonian constraint operator is proposed, offering better mathematical properties and applicability in loop quantum gravity and cosmology.

Findings

Operator is well-defined on diffeomorphism invariant states

Quantum algebra is anomaly-free on shell

Applicable to loop quantum cosmology, leading to new dynamics

Abstract

A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method, so that its regulated version in the kinematical Hilbert space is diffeomorphism covariant and creates new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.