A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and this author. To be able to apply the latter procedure to causal sets Sorkin’s ‘semantic switch’ from ‘partially ordered sets as finitary topological spaces’ to ...

We study the quantum Riemannian geometry of projective spaces any dimension. In particular, we compute Riemann and Ricci tensors using previously introduced metrics Levi-Civita connections. show that tensor is a bimodule map derive various consequences this fact. prove proportional to metric, giving analogue Einstein condition, corresponding scalar curvature.

Quantum real numbers are proposed by performing a quantum deformation of the standard real numbers IR. We start with the q-deformed Heisenberg algebra L̂q which is obtained by the Moyal ∗-deformation of the Heisenberg algebra generated by a and a. By representing L̂q as the algebras of q-differentiable functions, we derive quantum real lines from the base spaces of these functional algebras. We f...

We study certain principal actions on noncommutative C-algebras. Our main examples are the Zpand T-actions on the odd-dimensional quantum spheres, yielding as fixed-point algebras quantum lens spaces and quantum complex projective spaces, respectively. The key tool in our analysis is the relation of the ambient C-algebras with the Cuntz-Krieger algebras of directed graphs. A general result abou...

Open problems and recent results on causal completeness of probabilistic theories – p. 1/2 Structure Informal motivation of the problem of causal closedness: Reichenbach's Common Cause Principle Causal closedness of classical probability spaces (notion + propositions) Causal closedness – quantum probability spaces (notion + proposition) Spacelike correlations predicted by quantum field theory L...