Adaptation of the no-go theorem to parity-violating Maxwell-Chern-Simons electrodynamics

Determine whether the proof of the no-go theorem for repulsive Casimir forces can be adapted to Maxwell-Chern-Simons electrodynamics, whose bulk dynamics intrinsically violates parity.

Background

The paper studies Casimir interactions in (2+1)-dimensional Maxwell-Chern-Simons electrodynamics under several perfect electric, perfect magnetic, and infinitely permeable boundary conditions. Although the Chern-Simons term breaks parity, the authors find no repulsive Casimir force for the reflection-symmetric configurations considered, while the mixed PEC-PMC2 configuration produces a repulsive force but is not reflection-symmetric.

These results motivate the unresolved question of whether parity violation in the bulk can circumvent the established no-go theorem stating that repulsive Casimir forces require breaking reflection symmetry. The proposed problem concerns adapting the theorem's proof itself to a parity-violating Maxwell-Chern-Simons setting, rather than merely testing additional boundary configurations.