Hamiltonian constraint in Euclidean LQG revisited: First hints of off-shell Closure

Abstract

We initiate the hunt for a definition of Hamiltonian constraint in Euclidean Loop Quantum Gravity (LQG) which faithfully represents quantum Dirac algebra. Borrowing key ideas from previous works on Hamiltonian constraint in LQG and several toy models, we present some evidence that there exists such a continuum Hamiltonian constraint operator which is well defined on a suitable generalization of the Lewandowski-Marolf Habitat and is anomaly free off-shell.

68 pages, 6 figures

References in corpus (1)

• Lessons for Loop Quantum Gravity from Parametrised Field Theory

Cited by in corpus (5)

• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• An elementary introduction to loop quantum gravity
• Deformed covariance in spherically symmetric vacuum models of loop quantum gravity: Consistency in Euclidean and self-dual gravity
• Minisuperspace models of discrete systems