Pluriharmonic solutions to Yang-Mills equations: a $C^{\ast }$-algebras approach

Abstract

This partially expository paper provides a view of Yang-Mills equations from the perspective of complex variables, operator theory, and $C^{\ast }$-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.