Hamiltonian operator for loop quantum gravity coupled to a scalar field

TL;DR

This paper constructs a physical Hamiltonian operator in loop quantum gravity coupled to a scalar field, utilizing a new curvature operator and special loops, with detailed regularization and analysis of its action on spin networks.

Contribution

It introduces a novel Hamiltonian operator in loop quantum gravity with a specific regularization scheme using special loops and curvature operators.

Findings

The operator's action on spin network states is explicitly computed.

The regularization procedure is detailed and consistent.

Comments on the operator's properties and future directions are provided.

Abstract

We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on the idea of so-called "special loops". We discuss in detail the regularization procedure and the assignment of the loops, along with the properties of the resulting operator. We compute the action of the squared Hamiltonian operator on spin network states, and close with some comments and outlooks.