Hamiltonian operator for loop quantum gravity coupled to a scalar field

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.

Minor corrections implemented

References in corpus (4)

• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Gravity quantized
• Zakopane lectures on loop gravity
• A symmetric scalar constraint for loop quantum gravity

Cited by in corpus (7)

• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• An elementary introduction to loop quantum gravity
• Bouncing evolution in a model of loop quantum gravity
• Coherent 3j-symbol representation for the loop quantum gravity intertwiner space
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Graph coherent states for loop quantum gravity
• Fermion Doubling in Loop Quantum Gravity