Quantum representation of reduced twisted geometry in loop quantum gravity
Long G, Zhang C, Liu H (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 112
Pages Range: 1-21
Article Number: 024022
Journal Issue: 2
DOI: 10.1103/99fq-xz2w
Abstract
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge-invariant Hilbert space of loop quantum gravity. It is shown that the reduced twisted geometric variables not only describe the spatial discrete geometry more clearly, but also form a simple Poisson algebra which is analogous to that in quantum mechanics. By regularizing the reduced twisted geometric variables properly, the fundamental algebra of reduced twisted geometry is established, with the gauge-invariant Hilbert space in loop quantum gravity as the corresponding quantum representation space. This quantum representation also leads to fundamental operators associated with reduced twisted geometry. Based on these fundamental operators, a new type of extrinsic curvature operator is constructed in loop quantum gravity.
Involved external institutions
China (CN)How to cite
APA:
Long, G., Zhang, C., & Liu, H. (2025). Quantum representation of reduced twisted geometry in loop quantum gravity. Physical Review D, 112(2), 1-21. https://doi.org/10.1103/99fq-xz2w
MLA:
Long, Gaoping, Cong Zhang, and Hongguang Liu. "Quantum representation of reduced twisted geometry in loop quantum gravity." Physical Review D 112.2 (2025): 1-21.
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