  We investigate the effective field theory of a quantum chaotic billiard from
a new perspective of quantum anomalies, which result from the absence of
continuous spectral symmetry in quantized systems. It is shown that commutators
of composite operators on the energy shell acquire anomalous part. The presence
of the anomaly allows one to introduce effective dual fields as phase variables
without any additional coarse-graining nor ensemble averaging in a ballistic
system. The spectral Husimi function plays a role as the corresponding
amplitude.
