Summary
Plane non-Abelian propagating solutions of the classical Yang-Mills equations without external sources are obtained. The non-electromagneticlike properties of the waves, which arise from the non-linearities of the field equations, cause the energy-momentum vector density of the waves to be timelike.
Riassunto
Si ottengono soluzioni propagative, non Abeliane, piane delle equazioni classiche di Yang e Mills senza sorgenti esterne. Le proprietà di tipo non elettromagnetico delle onde, che sorgono dalle non linearità dell’equazioni del campo, fanno sí che la densità del vettore dell’energia-impulso delle onde sia del tipo temporale.
Реэюме
Получаются плоские неабелевы распространяюшиеся рещения для классических уравнений Янга-Миллса беэ внещних источников. Незлектромагнитно-п одобные свойства волн, которые воэникают иэ нелинейностей уравнений поля, приводят к тому, что векторная плотность знергии-импульса для зтих волн является времени-подобной.
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References
C. N. Yang andR. L. Mills:Phys. Rev.,96, 191 (1954).
C. A. Uzes:Journ. Math. Phys.,10, 1885 (1969).
H. G. Loos:Journ. Math. Phys.,8, 1870 (1967).
R. L. Ingraham:Nuovo Cimento,61 A, 73 (1969).
H. G. Loos:Journ. Math. Phys.,10, 2114 (1967).
R. P. Treat:Nuovo Cimento,50 A, 871 (1967).
There are a number of other possible choices pointed out byLoos (3), which yield internal holonomy groups (and also gauge groups) which are non-semi-simple or non-compact or both.
P. F. Byrd andM. D. Friedman:Handbook of Elliptic Integrals for Engineers and Physicists (Berlin, 1954).
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Partially supported by the West Virginia University Senate Committee on Research.
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Treat, R.P. Plane non-Abelian Yang-Mills waves. Nuov Cim A 6, 121–128 (1971). https://doi.org/10.1007/BF02728588
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DOI: https://doi.org/10.1007/BF02728588