Vacuum polarization of a massless field and conformal transformations

The rearrangement of the vacuum under special conformal transformations is studied in a conformally invariant theory of a quantized massless scalar field. This rearrangement is analogous to the Fulling–Unruh effect in a noninertial frame of reference. It is shown that there is a connection between the effect and the analytic properties of the complete system of solutions of the field equations that is chosen as basis for quantization in some coordinate system.