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We consider the gauge fixed partition function of pure $SU(N_c)$ gauge theoryin axial gauge following the Halpern's field strength formalism. We integrateover $3 (N_c^2-1)$ field strengths using the Bianchi identities and obtain aneffective action of the remaining $3 (N_c^2-1)$ field strengths in momentumspace. We obtain the static solutions of the equations of motion (EOM) of theeffective theory. The solutions exhibit Gaussian nature in the $z$ component ofmomentum and are proportional to the delta functions of the remainingcomponents of momentum. The solutions render a finite energy density of thesystem and the parameters are found to be proportional to fourth root of thegluon condensate. It indicates that the solutions offer a natural mass scale inthe low energy phase of the theory.

Stable, finite energy density solutions in the effective theory of non-abelian gauge fields