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Yang-Mills fields, Radon-Penrose transform and Cauchy-Riemann equations. (Russian) Zbl 0706.53047
The survey is devoted to the questions of complex analysis and mathematical physics in connection with Yang-Mills fields and Cauchy- Riemann equations. Principal subjects: Radon-Penrose gauge-fields transform (§§ 4,6), its ties with Faddeev type dispersion data (§ 5), Yang-Mills equations as compatibility conditions of linear equations with complex spectral parameter (§ 1,2), Yang-Mills equations in terms of the $${\bar \partial}$$-equation on distance data (§ 7,8); interpretation of the solutions of Yang-Mills-Higgs-Dirac equations by holomorphic vector bundles over the manifold of complex light lines (§§ 7,8,9).
Reviewer: M.Rahula

##### MSC:
 53C80 Applications of global differential geometry to the sciences 81T13 Yang-Mills and other gauge theories in quantum field theory 32V05 CR structures, CR operators, and generalizations