A proposal for the algebra of a novel noncommutative spacetime

Fröb M, Much A, Papadopoulos K (2026)

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2026

Publisher: arXiv

DOI: 10.48550/arXiv.2601.07350

We investigate the quantum structure of spacetime at fundamental scales via a novel,

Lorentz-invariant noncommutative coordinate framework. Building on insights from noncom-

mutative geometry, spectral theory, and algebraic quantum field theory, we systematically

construct a quantum spacetime algebra whose geometric and causal properties are derived

from first principles. Using the Weyl algebra formalism and the Gelfand–Naimark–Segal

(GNS) construction, we rigorously define operator-valued coordinates that respect Lorentz

symmetry and encode quantum gravitational effects through nontrivial commutation rela-

tions. We show how the emergent quantum spacetime exhibits minimal length effects, which

deliver both classical Minkowski distances and quantum corrections proportional to the

Planck length squared. Furthermore, we establish that noncommutativity respects a fuzzy

form of causality, where the quantum causal structure gives back the light cone in the clas-

sical limit, vanishing for spacelike separations and encoding a time orientation for timelike

intervals.

Markus Fröb Lehrstuhl für Mathematik (Operatoralgebren) (Heisenberg-Professur)

APA:

Fröb, M., Much, A., & Papadopoulos, K. (2026). A proposal for the algebra of a novel noncommutative spacetime. (Unpublished, Submitted).

MLA:

Fröb, Markus, Albert Much, and Kyriakos Papadopoulos. A proposal for the algebra of a novel noncommutative spacetime. Unpublished, Submitted. 2026.

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