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<p>This partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40627_2025_175_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>C</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>-algebras. Through operator-valued pluriharmonic and skew-Hermitian differential forms, it constructs a new class of instanton solutions. Furthermore, it provides a complex variable version of the Yang-Mills Lagrangian and the Belavin-Polyakov-Schwartz-Tyupkin instanton.</p>

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Pluriharmonic solutions to Yang-Mills equations: A \(C^*\)-algebra approach

  • 期刊论文

  • 发表日期：

    2025年10月17日

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  • Marius Beceanu,
  • Sachin Munshi,
  • Rongwei Yang

摘要

This partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and \(C^{*}\) C ∗ -algebras. Through operator-valued pluriharmonic and skew-Hermitian differential forms, it constructs a new class of instanton solutions. Furthermore, it provides a complex variable version of the Yang-Mills Lagrangian and the Belavin-Polyakov-Schwartz-Tyupkin instanton.