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The covariantly constant gauge fields are solutions of the sourcelessYang-Mills equation and represent the classical vacuum fields. We found thatthe moduli space of covariantly constant gauge fields is much larger than thespace of constant chromomagnetic and chromoelectric fields. A wider class ofcovariantly constant gauge field solutions is obtained through the nontrivialspace-time dependence of the unit colour vector that provides an additionalcontribution to the field strength tensor. This new class of covariantlyconstant gauge field solutions can be constructed by using the generalproperties of the Cho Ansatz. We define the topological currents and thecorresponding charges and demonstrate that the new solutions have zero monopolecharge density. Instead, the solutions have nonzero Hopf invariant, which isthe magnetic helicity of the Faraday force lines.

How Large is the Space of Covariantly Constant Gauge Fields