Application of Clifford algebra to analysis of spin properties of semiconductors

Abstract

The quantum mechanics is formulated in terms of state vectors in the Hilbert space and operators that act on these vectors. However, using the Clifford algebra an alternative formulation is possible, where multivectors in n-dimensional linear Euclidean space represent both the state of the system and quantum operators. In this report a short overview is presented on how the Clifford algebra can be used to investigate electron and hole spin properties in semiconductors. In particular, calculation of free electron and hole spin precession in cubic semiconductors with the help of the Clifford algebra is discussed.
Keywords: Clifford algebra, geometric algebra, cubic semiconductors, spintronics
PACS: 75.10.Jm, 85.75.-d, 72.25.Dc, 71.70.Ej