New scalar constraint operator for loop quantum gravity

Understand

We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity.

• The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator.
• To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops.
• The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work.