59 citations · 348 across the 28 of their papers we have counts for
11 papers · 1 filter
Generally covariant -particle dynamics
Tomasz Miller, Michał Eckstein, Paweł Horodecki +1
A simultaneous description of the dynamics of multiple particles requires a configuration space approach with an external time parameter. This is in stark contrast with the relativ…
Spectral Action in Noncommutative Geometry
Michał Eckstein, Bruno Iochum
What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes,…
The noncommutative geometry of Zitterbewegung
Michał Eckstein, Nicolas Franco, Tomasz Miller
Based on the mathematics of noncommutative geometry, we model a 'classical' Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of th…
Causality for nonlocal phenomena
Michał Eckstein, Tomasz Miller
Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explor…
Causality in noncommutative two-sheeted space-times
Nicolas Franco, Michał Eckstein
We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for c…
Asymptotic and exact expansions of heat traces
Michał Eckstein, Artur Zając
We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existe…