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

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 $V_i^a=B_i^a(C)+D_i(C){\varphi }^a$ 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.

6 pages, no figures, revtex

References in corpus (2)

• Yang-Mills Fields and Riemannian Geometry
• Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories

Cited by in corpus (1)

• An algebraic method for solving the SU(3) Gauss law