31 citations · 105 across the 13 of their papers we have counts for
13 papers
Einstein Algebras in a Categorical Context
Leszek Pysiak, Wiesław Sasin, Michael Heller +1
According to the basic idea of category theory, any Einstein algebra, essentially an algebraic formulation of general relativity, can be considered from the point of view of any ob…
Causal evolution of probability measures and continuity equation
Tomasz Miller
We study the notion of a causal time-evolution of a conserved nonlocal physical quantity in a globally hyperbolic spacetime . The role of the `global time' is played b…
Reproducing Kernel Hilbert Space Associated with a Unitary Representation of a Groupoid
Monika Drewnik, Tomasz Miller, Zbigniew Pasternak-Winiarski
The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More…
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…
Functorial differential spaces and the infinitesimal structure of space-time
Leszek Pysiak, Wiesław Sasin, Michael Heller +1
We generalize the differential space concept as a tool for developing differential geometry, and enrich this geometry with infinitesimals that allow us to penetrate into the superf…
Operational causality in spacetime
Michał Eckstein, Paweł Horodecki, Ryszard Horodecki +1
The no-signalling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood…
Time functions and -causality between measures
Tomasz Miller
Employing the notion of a coupling between measures, drawn from the optimal transport theory, we study the extension of the Sorkin-Woolgar causal relation onto the space $\ma…
On the causality and -causality between measures
Tomasz Miller
Drawing from our earlier works on the notion of causality for nonlocal phenomena, we propose and study the extension of the Sorkin--Woolgar relation onto the space of Borel p…
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…
Causal evolution of wave packets
Michał Eckstein, Tomasz Miller
Drawing from the optimal transport theory adapted to the relativistic setting we formulate the principle of a causal flow of probability and apply it in the wave packet formalism.…
Polish spaces of causal curves
Tomasz Miller
We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the…
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…
Generalized derivations and general relativity
M. Heller, T. Miller, L. Pysiak +1
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra . Such a derivation, introduced by Bresar in 1991, is give…