# Casimir Effect, Theta Vacuum and Topological Order in QED

**Abstract**: We analyze the case where one imposes non-trivial spatal topology for a simple abelian gaug theory. As usual,the large gauge transformatons present in the system allow one to discuss theta vacuum and magneto-electric effect via the theta term. However, even for zero theta parameter, the tunneling transitions between different topologically inequivalent pre-vacua give rise to an additional contribution to vacuum energy that can be measured in the context of Casimir effect. Furthermore, photon production and non-trivial electric and magnetic responses can be induced by applying a global external field which behaves similar to an effective theta parameter. The theory in the far IR can be described by a TQFT and a phase transition occurs at effective theta = pi where the quantum vacuum has degeneracy two. Possible experimental implementations will also be discussed.

**Series:**IQIM Postdoctoral and Graduate Student Seminar Series