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

Pushan Majumdar·H. S. Sharatchandra
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Abstract

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) ϕ^{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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Pushan Majumdar, H. S. Sharatchandra. 1998-04-20. General Solution of the non-abelian Gauss law and non-abelian analogs of the Hodge decomposition. https://doi.org/10.1103/physrevd.58.067702

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