# Generalized uncertainty principle in graphene

## TL;DR

This paper explores how extending the low-energy approximation in graphene leads to a generalized Dirac field theory aligned with a modified uncertainty principle, with implications for noncommutative geometry and physical realization.

## Contribution

It introduces a generalized Dirac Hamiltonian for graphene that incorporates a modified uncertainty principle beyond the linear dispersion approximation.

## Key findings

- Derived a generalized Dirac Hamiltonian for graphene
- Linked the Hamiltonian to a generalized uncertainty principle
- Discussed potential physical realizations and noncommutative geometry

## Abstract

We show that, by going beyond the low-energy approximation for which the dispersion relations of graphene are linear, the corresponding emergent field theory is a specific generalization a Dirac field theory. The generalized Dirac Hamiltonians one obtains are those compatible with specific generalizations of the uncertainty principle. We also briefly comment on the compatibility of the latter with noncommuting positions, $[x_i,x_j] \neq 0$, and on their possible physical realization.