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Spherically Symmetric Chromostatic Condensates as an Introduction to the Strong Conjecture for Color Confinement

Nonlinearities imbedded in the Lagrange density for non-Abelian gauge theories produce solutions to the Yang-Mills Maxwell equations that describe spatially extended chromostatic condensates. For solutions in spherically-symmetric SU(2) the topological structures separating such condensates provide a specific solitonic description of color confinement. The strong Conjecture The confinement mechanism for QCD involves a domain wall of topological (CP-odd) charge separating the interior volume of hadrons from an exterior volume. To explain the consequences of this conjecture we describe spherically symmetric chromostatic condensates that are consistent with the interior volume of a hadron and other condensates that are consistent with exterior vacuum volume. We then demonstrate how the Yang-Mills Maxwell equations can connect the two volumes with a soliton domain wall. The preliminary phenomenological description described here does not deal explicitly either with charged fermions or with the quantization of non-Abelian dynamics.