Quantum Flatland and Monolayer Graphene from a Viewpoint of Geometric Algebra
A. Dargys
Center for Physical Sciences and Technology, Semiconductor Physics Institute, A. GoŇ°tauto 11, LT-01108 Vilnius, Lithuania
Received: May 11, 2013
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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 Cl3,0 and Cl2,0 are applied to analyze relativistic properties of the graphene. It is shown that only three-dimensional Cl3,0 rather than two-dimensional Cl2,0 algebra is compatible with a relativistic flatland.

DOI: 10.12693/APhysPolA.124.732
PACS numbers: 73.43.Cd, 81.05.U-, 03.65.Pm