Algebraic description of spacetime foam

2001/02/28 by Ioannis Raptis, Roman R. Zapatrin, Roman R Zapatrin · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic number #Commutative property #Formalism (music) #General relativity #Limit (mathematics) #Mathematics of general relativity #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Spacetime #Spacetime topology #Theory of relativity #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/18/20/303

published as Class.Quant.Grav. 18 (2001) 4187-4212 · 34 pages, LaTeX2e, the section concerning classical spacetimes in the limit essentially corrected

arxiv created 2001/07/11 · openalex publication_date 2001/10/04 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.

Citations

• Causality Implies the Lorentz Group
• General relativity without coordinates
• Physik und realität
• Finitary substitute for continuous topology
• ?Superconducting? causal nets

Cited by

• A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity
• ‘Third’ Quantization of Vacuum Einstein Gravity and Free Yang–Mills Theories