  We discuss the boundary effect of anomaly-induced action in two-dimensional
spacetime, which is ignored in previous studies. Anomaly-induced action, which
gives the stress tensor with the same trace as the trace anomaly, can be
represented in terms of local operators by introducing an auxiliary scalar
field. Although the degrees of freedom of the auxiliary field can in principle
describe the quantum states of the original field, the principal relation
between them was unclear. We show here that, by considering the boundary
effect, the solutions of classical auxiliary fields are naturally related to
the quantum states of the original field. We demonstrate this conclusion via
several examples such as the flat, black hole and the de Sitter spacetime.
