  First conformal transformations of the $S$-matrix are derived in massless
$\phi^4$-theory. Then it is shown that the anomalous transformations can be
rewritten as a symmetry once one has introduced a local coupling and interprets
the charge of the symmetry accordingly. By introducing a suitable effective
coupling on which the $S$-matrix depends one is able to identify via the
$\beta$-function an underlying new spacetime with non-trivial conformal (flat)
metric.
