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arXiv · 2604.19549

Fuzzy Geometries with an Internal Space

John W. Barrett·Joseph Burridge
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Abstract

The product of a non-commutative matrix spectral triple with a simple two-dimensional internal space is considered. This is interpreted as a non-commutative spacetime that contains one charged Dirac fermion and its antiparticle. The inner fluctuations of a vacuum Dirac operator are calculated, using the standard technique of Connes' one-forms. This results in the non-commutative analogue of a gauge field, as expected, and also fluctuations of the spacetime geometry. In addition, the fluctuations include a derivative operator that depends on the particle charge. The integral over the fermions in the model is calculated, leading to some novel induced bosonic terms.

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John W. Barrett, Joseph Burridge. 2026-04-21. Fuzzy Geometries with an Internal Space. https://arxiv.org/abs/2604.19549

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