On Spectral Triples in Quantum Gravity II
Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
TL;DR
This paper constructs a semifinite spectral triple for an algebra related to canonical quantum gravity, using loop-based algebraic structures, providing a new mathematical framework within Loop Quantum Gravity.
Contribution
It introduces a semifinite spectral triple associated with loop-based algebras in quantum gravity, advancing the mathematical tools in the field.
Findings
Spectral triple constructed for loop algebra in quantum gravity
Algebra generated by based loops in triangulation and subdivisions
Provides a gauge-fixed perspective of Loop Quantum Gravity
Abstract
A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Black Holes and Theoretical Physics · Advanced Topics in Algebra