  We illustrate with examples that quantum symmetry breakings in perturbation
theory are connected to breakdown of momentum routing invariance (MRI) in the
loops of a Feynman diagram. We show that MRI is a necessary and sufficient
condition to preserve abelian gauge symmetry at arbitrary loop order. We adopt
the implicit regularization framework in which surface terms that are directly
connected to momentum routing can be constructed to arbitrary loop order. The
interplay between momentum routing invariance, surface terms and anomalies is
discussed. We also illustrate that MRI is important to preserve supersymmetry.
For theories with poor symmetry content, such as scalar field theories, MRI is
shown to be important in the calculation of renormalization group functions.
