0 Trace anomaly and Casimir effect

The Casimir energy for scalar field of two parallel conductor in two dimensional domain wall background with Dirichlet boundary conditions is calculated by making use of general properties of renormalized stress tensor.We show that vacuum expectation values of stress tensor contain two terms which come from the boundary conditions and the gravitational background. In two dimensions the minimal coupling reduces to the conformal coupling and stress tensor is obtainable by the local and non local contribution of the anomalous trace.It is in close relation to what is done in [11] [12]. This work shows that there exists a subtle relation between casimir effect and trace anomaly in curved spacetime.