General Solution of the non-abelian Gauss law and non-abelian analogs of the Hodge decomposition

Details General Solution of the non-abelian Gauss law and non-abelian analogs of the Hodge decomposition General Solution of the non-abelian Gauss law and non-abelian analogs of the Hodge decomposition

1998-04-20

arxiv.org/abs/hep-th/9804128v1

Phys.Rev. D58 (1998) 067702

Physics

High Energy Physics

High Energy Physics - Theory

6 pages, no figures, revtex

Scientific paper

10.1103/PhysRevD.58.067702

General solution of the non-abelian Gauss law in terms of covariant curls and gradients is presented. Also two non-abelian analogs of the Hodge decomposition in three dimensions are addressed. i) Decomposition of an isotriplet vector field $V_{i}^{a}(x)$ as sum of covariant curl and gradient with respect to an arbitrary background Yang-Mills potential is obtained. ii) A decomposition of the form $V_{i}^{a}=B_{i}^{a}(C)+D_{i}(C) \phi^{a} $ which involves 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.

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