Weyl anomaly of 2D dilaton scalar gravity and the Hermiticity of the system operator

The Weyl (conformal) anomaly in the dilaton-scalar system in 2-dimensional gravity is examined. We take the heat-kernel regularization for the ultraviolet divergences. Generally the Weyl anomaly is determined by the second order differential (elliptic) operator of the system and the definition of the measure, We have the freedom of the operator choice caused by the arbitrariness of total divergences (surface terms) in the action. We focus on such points and the Hermiticity of the system operator.