Analytic evaluation of the PMC Casimir-energy integrals

Derive an analytic solution of the momentum integrals defining the Gribov–Zwanziger Casimir energy for parallel perfect magnetic conductor plates, rather than relying on numerical evaluation for specified plate separation and Gribov parameter.

Background

The functional-integral calculation expresses the PMC Casimir energy as the sum of two one-dimensional momentum integrals, involving complex square-root frequencies determined by the Gribov parameter. These integrals describe the nonperturbative modification of the Casimir interaction induced by the Gribov–Zwanziger gluon propagator.

The paper evaluates these expressions numerically and analyzes their dependence on the plate separation and Gribov parameter, but does not obtain closed-form analytic expressions. An analytic evaluation could clarify the asymptotic behavior and the relation to the Yang–Mills limit.