2009/11/12 by Johannes Aastrup, Aastrup, Johannes, Jesper M. Grimstrup +4
Mathematics · Physics and Astronomy · #Advanced Operator Algebra 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 #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.0911.2404
one figure
arxiv created 2009/11/12 · openalex publication_date 2009/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We modify the construction of the spectral triple over an algebra of holonomy loops by introducing additional parameters in form of families of matrices. These matrices generalize the already constructed Euler-Dirac type operator over a space of connections. We show that these families of matrices can naturally be interpreted as parameterizing foliations of 4-manifolds. The corresponding Euler-Dirac type operators then induce Dirac Hamiltonians associated to the corresponding foliation, in the previously constructed semi-classical states.