Casimir effect on nontrivial topology spaces in Krein space quantization

Casimir effect of a topologically nontrivial two-dimensional space-time, through Krein space quantization [1,2], has been calculated. In other words, auxiliary negative norm states have been utilized here. Presence of negative norm states play the role of an automatic renormalization device for the theory. The negative norm states (which do not interact with the physical world) could be chosen in two perspective. In the first case our method results in zero or vanishing values for energy. In the second case, however, the result are the same as the renormalization procedure.