Noncommutative geometrical origin of the energy-momentum dispersion relation
Mathematical Physics
2017-02-02 v2 High Energy Physics - Theory
math.MP
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.
Keywords
Cite
@article{arxiv.1611.05810,
title = {Noncommutative geometrical origin of the energy-momentum dispersion relation},
author = {Apimook Watcharangkool and Mairi Sakellariadou},
journal= {arXiv preprint arXiv:1611.05810},
year = {2017}
}