Non-Commutative Topology for Curved Quantum Causality
| dc.creator | Raptis, Ioannis | |
| dc.date | 2001-01-19 | |
| dc.date | 2001-02-22 | |
| dc.date.accessioned | 2026-07-07T03:25:36Z | |
| dc.date.available | 2026-07-07T03:25:36Z | |
| dc.description | A quantum causal topology is presented. This is modeled after a non-commutative scheme type of theory for the curved finitary spacetime sheaves of the non-abelian incidence Rota algebras that represent `gravitational quantum causal sets'. The finitary spacetime primitive algebra scheme structures for quantum causal sets proposed here are interpreted as the kinematics of a curved and reticular local quantum causality. Dynamics for quantum causal sets is then represented by appropriate scheme morphisms, thus it has a purely categorical description that is manifestly `gauge-independent'. Hence, a schematic version of the Principle of General Covariance of General Relativity is formulated for the dynamically variable quantum causal sets. We compare our non-commutative scheme-theoretic curved quantum causal topology with some recent $C^{*}$-quantale models for non-abelian generalizations of classical commutative topological spaces or locales, as well as with some relevant recent results obtained from applying sheaf and topos-theoretic ideas to quantum logic proper. Motivated by the latter, we organize our finitary spacetime primitive algebra schemes of curved quantum causal sets into a topos-like structure, coined `quantum topos', and argue that it is a sound model of a structure that Selesnick has anticipated to underlie Finkelstein's reticular and curved quantum causal net. At the end we conjecture that the fundamental quantum time-asymmetry that Penrose has expected to be the main characteristic of the elusive `true quantum gravity' is possibly of a kinematical or structural rather than of a dynamical character, and we also discuss the possibility of a unified description of quantum logic and quantum gravity in quantum topos-theoretic terms. | |
| dc.description | 65 pages, LaTeX2e,typos corrected | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0101082 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0101082 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33776 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Non-Commutative Topology for Curved Quantum Causality | |
| dc.type | text |