Graphical method in loop quantum gravity: II. The Hamiltonian constraint and inverse volume operators

Abstract

This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin network states with trivalent vertices. Both of the operators involve the co-triad operator which contains holonomies by construction. The non-ambiguous, concise and visual characters of our graphical method ensure the rigour for our calculations. Our results indicate some corrections to the existing results in literatures.

18 pages; a few modifications

References in corpus (3)

• New Hamiltonian constraint operator for loop quantum gravity
• Quantum spin dynamics
• Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator

Cited by in corpus (4)

• New volume and inverse volume operators for loop quantum gravity
• Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
• Introduction to SU(2) recoupling theory and graphical methods for loop quantum gravity
• Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator