▎ 摘　　要

Quantum mechanical properties of the graphene are, as a rule, treated within the Hilbert space formalism. However a different approach is possible using the geometric algebra, where quantum mechanics is done in a real space rather than in the abstract Hilbert space. In this article the geometric algebra is applied to a simple quantum system, a single valley of monolayer graphene, to show the advantages and drawbacks of geometric algebra over the Hilbert space approach. In particular, 3D and 2D Euclidean space algebras Cl-3,Cl-0 and Cl-2,Cl-0 are applied to analyze relativistic properties of the graphene. It is shown that only three-dimensional Cl-3,Cl-0 rather than two-dimensional Cl-2,Cl-0 algebra is compatible with a relativistic flatland.