51 citations · 225 across the 16 of their papers we have counts for
16 papers
Pseudo-Riemannian spectral triples and the harmonic oscillator
Koen van den Dungen, Mario Paschke, Adam Rennie
We define pseudo-Riemannian spectral triples, an analytic context broad enough to encompass a spectral description of a wide class of pseudo-Riemannian manifolds, as well as their…
Quantum Gravity coupled to Matter via Noncommutative Geometry
Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gra…
On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge in a semi-classical approximation from a abstract spectral triple construction. The spectral triple is c…
Emergent Dirac Hamiltonians in Quantum Gravity
Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
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…
On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke +1
We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classic…
Equivariant Lorentzian Spectral Triples
Mario Paschke, Andrzej Sitarz
We present examples of equivariant noncommutative Lorentzian spectral geometries. The equivariance with respect to a compact isometry group (or quantum group) allows to construct t…