Covariant Poisson equation with compact Lie algebras

Details Covariant Poisson equation with compact Lie algebras Covariant Poisson equation with compact Lie algebras

2002-11-13

arxiv.org/abs/math-ph/0211024v1

J.Math.Phys. 45 (2004) 2844-2863

Physics

Mathematical Physics

31 pages, LaTeX2e

Scientific paper

10.1063/1.1763001

The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for the existence and smoothness of solutions to the covariant Poisson equation. These conditions require, apart from suitable continuity, appropriate local integrability of the gauge potentials and global weighted integrability of the curvature form and the source. The possibility of nontrivial asymptotic behaviour of a solution is also considered. As a by-product, weighted covariant generalisations of Sobolev embeddings are established.

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