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arXiv · 1611.05810

Noncommutative geometrical origin of the energy-momentum dispersion relation

Apimook Watcharangkool·Mairi Sakellariadou
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Abstract

We investigate a link between the energy-momentum dispersion relation and the spectral distance in the context of a Lorentzian almost-commutative spectral geometry, defined by the product of Minkowski spacetime and an internal discrete noncommutative space. Using the causal structure, the almost-commutative manifold can be identified with a pair of four-dimensional Minkowski spacetimes embedded in a five-dimensional Minkowski geometry. Considering fermions travelling within the light cone of the ambient five-dimensional spacetime, we then derive the energy-momentum dispersion relation.

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Apimook Watcharangkool, Mairi Sakellariadou. 2016-11-17. Noncommutative geometrical origin of the energy-momentum dispersion relation. https://doi.org/10.1103/physrevd.95.025027

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