Categorical Operator Algebraic Foundations of Relational Quantum Theory
Abstract
We provide an algebraic formulation of C.Rovelli's relational quantum theory that is based on suitable notions of "non-commutative" higher operator categories, originally developed in the study of categorical non-commutative geometry. As a way to implement C.Rovelli's original intuition on the relational origin of space-time, in the context of our proposed algebraic approach to quantum gravity via Tomita-Takesaki modular theory, we tentatively suggest to use this categorical formalism in order to spectrally reconstruct non-commutative relational space-time geometries from categories of correlation bimodules between operator algebras of observables. Parts of this work are joint collaborations with: Dr.Roberto Conti (Sapienza Universita' di Roma), Assoc.Prof.Wicharn Lewkeeratiyutkul (Chulalongkorn University, Bangkok), Dr.Rachel Dawe Martins (Istituto Superior Tecnico, Lisboa), Dr.Matti Raasakka (Paris 13 University), Dr.Noppakhun Suthichitranont.
Keywords
Cite
@article{arxiv.1412.7256,
title = {Categorical Operator Algebraic Foundations of Relational Quantum Theory},
author = {Paolo Bertozzini},
journal= {arXiv preprint arXiv:1412.7256},
year = {2025}
}
Comments
6 pages, AMS-LaTeX2e. Submitted to PoS by SISSA for the proceedings of the FFP14 symposium "Frontiers of Fundamental Phyisics 14", 15-18 July 2014, Aix Marseille University, Marseille, France