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<p>This paper deals with applications of K-theory to solid state physics. Main attention is paid to the topological insulators characterized by having a broad energy gap stable under small deformations. The algebras of observables of such solid bodies belong to the class of graded <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40590_2025_753_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras for which there is a variant of K-theory proposed by Van Daele. It makes possible to define the topological invariants of insulators in K-theory terms.</p>

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\(C^*\) and Clifford algebras in solid state physics

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Armen Sergeev

摘要

This paper deals with applications of K-theory to solid state physics. Main attention is paid to the topological insulators characterized by having a broad energy gap stable under small deformations. The algebras of observables of such solid bodies belong to the class of graded \(C^*\) C ∗ -algebras for which there is a variant of K-theory proposed by Van Daele. It makes possible to define the topological invariants of insulators in K-theory terms.