Casimir effect in a two dimensional signature changing spacetime

We study the Casimir effect for free massless scalar fields propagating on a two-dimensional cylinder with a metric that admits a change of signature from Lorentzian to Euclidean. We obtain a nonzero pressure, on the hypersurfaces of signature change, which destabilizes the signature changing region and so alters the energy spectrum of scalar fields. The modified region and spectrum, themselves, back react on the pressure. Moreover, the central term of diffeomorphism algebra of corresponding infinite conserved charges changes correspondingly.