  We analyze, from a canonical quantum field theory perspective, the problem of
one-dimensional particles with three-body attractive interactions, which was
recently shown to exhibit a scale anomaly identical to that observed in
two-dimensional systems with two-body interactions. We study in detail the
properties of the scattering amplitude including both bound and scattering
states, using cutoff and dimensional regularization, and clarify the connection
between the scale anomaly derived from thermodynamics to the non-vanishing
nonrelativistic trace of the energy-momentum tensor.
