An algebra of the Yang‐Mills field
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6.In all that follows, Greek indices run over (1,2,3,4), lower case Latin indices run over (1,2,3), and upper case Latin indices refer to the internal symmetry space which is usually left unspecified. We take the Minkowski metric Tneusual summation convention is assumed. The and of Ref. 1 are related to quantities defined here by and
7.R. Utiyama, Phys. Rev. 101, 1597 (1956).
8.See W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison‐Wesley, Reading, Mass., 1955).
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9.I am grateful to Professor H. Brown and Professor R. Brown of The Ohio State University for valuable discussions of this paper.
10.As long as there is one element x such that then this element can be “normalized” to give a unit.
11.The vector potential used here differs by exactly a sign from that defined in many texts, e.g., Ref. 8. This sign difference has no effect on the equations for the electric and magnetic field intensities; our choice allows the electric field intensity to be expressed as the spatial part of the 4‐curl of A.
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