Reduced form of Yang-Mills equation of \(SU(2)\) on \(R^{3,1}\) (Q2747398)
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scientific article; zbMATH DE number 1657686
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reduced form of Yang-Mills equation of \(SU(2)\) on \(R^{3,1}\) |
scientific article; zbMATH DE number 1657686 |
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16 November 2002
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Yang-Mills equation
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differential linear transformation
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Wu elimination
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Reduced form of Yang-Mills equation of \(SU(2)\) on \(R^{3,1}\) (English)
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After Yang and Mills extended, in 1954, the concept of gauge-invariance to the non-Abelian groups, a huge theoretical effort has been invested in these fields, since they are considered to be the best candidates in describing the main interactions in nature and their interplay. The aim of the present paper is to derive a differential linear transformation which brings the SU(2) Yang-Mills equation on the Minkowski four-dimensional spacetime to a reduced form, expressed in terms of the d'Alembert and some linear differential operators. It turns out that any solution \(u(x)\), \(v(x)\), \(w(x)\) of this d'Alembert operator will provide a solution to the 12 Yang-Mills equations YM\(jk=0\), with \(j=1,2,3,4\) and \(k=1,2,3\).
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