Lorentz and gauge invariance of quantum space

TL;DR

This paper proposes a discrete model of space that maintains Lorentz and gauge invariance, linking generalized uncertainty principles to electromagnetic interactions, and suggests this discreteness could explain natural crystal structures.

Contribution

It introduces a Lorentz and gauge invariant discrete space model derived from GUP and electromagnetic interaction equivalence in the Dirac equation.

Findings

Derived a wavefunction solution satisfying the equivalence

Proposed a discrete space model consistent with Lorentz and gauge symmetry

Suggested a connection between space discreteness and natural crystal structures

Abstract

Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic interaction term in Dirac equation. We derived a wavefunction solution that satisfies this equivalency. This discreteness may explain the crystal and quasicrystal structures observed in nature at different energy scales.