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Implementation of the holonomy representation of the Ashtekar connection in loop quantum gravity

2020/12/28 by Jakub Bilski, Bilski, Jakub
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2012.14441

openalex publication_date 2020/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The improved lattice regularization method of the Ashtekar connection holonomy representation in loop quantum gravity is described in this article. The approach is based on the geometric expansion of holonomies into power series up to the quadratic order terms in the regularization parameter. As a result, a more accurate procedure than the currently established approach to the canonical lattice quantization of gravity is obtained. Moreover, if holonomies are defined along linear links, this procedure becomes exact. Furthermore, in the improved method, the symmetry of holonomies assigned to links is directly reflected in the related distribution of connections. Finally, the domain of the lattice-regularized Hamiltonian constraint takes a natural structure of elementary cells sum. Consequently, under certain restrictions, the related scalar constraint operator, which spectrum is independent of intertwiners, can be defined.

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