2019/10/04 by Johannes Aastrup, Aastrup, Johannes, Jesper Møller Grimstrup +1
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) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1910.01841
openalex publication_date 2019/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct a non-commutative geometry over a configuration\nspace of gauge connections and show that it gives rise to a candidate for an\ninteracting, non-perturbative quantum gauge theory coupled to a fermionic field\non a curved background. The non-commutative geometry is given by an\ninfinite-dimensional Bott-Dirac type operator, whose square gives the Hamilton\noperator, and which interacts with an algebra generated by\nholonomy-diffeomorphisms. The Bott-Dirac operator and the associated Hilbert\nspace relies on a metric on the configuration space of connections, which\neffectively works as a covariant ultra-violet regulator. We show that the\nconstruction coincides with perturbative quantum field theory in a local limit.\nQuestions concerning Lorentz invariance and the fermionic sector as well as the\nissue of existence are left open.\n