A generalized Hamiltonian constraint operator in loop quantum gravity and its simplest Euclidean matrix elements

2000/11/30 by Marcus Gaul, Carlo Rovelli · 8 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Neutrino Physics Research #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/18/9/301

published as Class.Quant.Grav. 18 (2001) 1593-1624 · 35 pp, 20 eps figures; minor corrections, references added; version to appear in Class. Quant. Grav

arxiv created 2001/03/08 · openalex publication_date 2001/04/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We study a generalized version of the Hamiltonian constraint operator in non-perturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU (2) representations in the regularization of the operator, in contrast to the original definition where only the fundamental representation is taken. This leads to a quantization ambiguity and to a family of operators with the same classical limit. We calculate the action of the Euclidean part of the generalized Hamiltonian constraint on trivalent states, using the graphical notation of Temperley-Lieb recoupling theory. We discuss the relation between this generalization of the Hamiltonian constraint and crossing symmetry.

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