TL;DR
This paper investigates how scalar fields propagate on a random lattice, deriving dispersion relations through a limiting process from periodic lattices, with specific calculations for a one-dimensional model.
Contribution
It introduces a method to compute dispersion relations for scalar fields on random lattices by taking limits of periodic lattices, relevant for quantum gravity phenomenology.
Findings
Derived dispersion relation coefficients for a 1D model.
Established a procedure to analyze wave propagation on random lattices.
Provided insights into quantum gravity phenomenology.
Abstract
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic lattice. We use this to calculate the lowest order coefficients of the dispersion relation for a specific one-dimensional model.
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