Phys. Rev. D 58, 067702 (1998) [3 pages]General solution of the non-Abelian Gauss law and non-Abelian analogues of the Hodge decompositionReceived 21 April 1998; published 5 August 1998 A general solution of the non-Abelian Gauss law in terms of covariant curls and gradients is presented. Also two non-Abelian analogues of the Hodge decomposition in three dimensions are addressed: (i) A decomposition of an isotriplet vector field Via(x) as the sum of a covariant curl and gradient with respect to an arbitrary background Yang-Mills potential is obtained; (ii) a decomposition of the form Via=Bia(C)+Di(C)φa which involves a non-Abelian magnetic field of a new Yang-Mills potential C is also presented. These results are relevant for duality transformation for non-Abelian gauge fields. © 1998 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.58.067702
DOI:
10.1103/PhysRevD.58.067702
PACS:
11.15.-q
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