Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
arXiv:1602.06086 · doi:10.1103/PhysRevD.94.045004
Abstract
We give a gauge-covariant decomposition of the Yang-Mills field with an exceptional gauge group , which extends the field decomposition invented by Cho, Duan-Ge, and Faddeev-Niemi for the Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of . The resulting new form is used to define gauge-invariant magnetic monopoles in the Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semi-simple Lie group other than and .
20 pages, 4 figures, minor changes (Appendix C and references added), a version accepted for publication in Physical Review D
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