K-Theory Methods in Solid State Physics

This paper is a review of K-theory methods in solid state physics. Our goal is to demonstrate that K-theory is a natural language for the mathematical description of solid bodies. Our main tool is the K-theory of C*-algebras. We follow Kitaev’s idea that the symmetry algebras of solid bodies belong to the class of Clifford algebras which reduces the quantization problem for solid states to the representation theory of Clifford algebras.