Casimir effect in Yang-Mills theories in three and four dimensions

We calculate the Casimir energy for the configuration of two parallel plates coupled to non-Abelian gauge fields with a Yang-Mills action. We consider both 2 + 1 and 3 + 1 dimensions in the manifestly gauge-invariant formalism we have pursued over the last several years which allows us to factor out the gauge degrees of freedom. A boundary action in the functional integral, equivalent to the insertion of operators representing the plates, is used to enforce the required boundary conditions for the gauge fields. The result is for a kinematic regime corresponding to the exchange of gluons with a dynamically generated mass. We find good agreement in 2 + 1 dimensions and reasonable agreement in 3 + 1 dimensions with lattice-based numerical evaluations.