On a formal, fundamental level in a non-Abelian gauge theory only
composite fields can be gauge-invariant, rather than the elementary
fields employed in perturbation theory. While at first sight in
contradiction to the phenomenological success of perturbation theory in
electroweak physics, there is a deeper reason for both being compatible,
the Fröhlich-Morchio-Strocchi mechanism. Its working and validity hasbeen demonstrated explicitly in lattice simulations. However, even then
this leaves still room for new phenomena in the standard model.
Moreover, the standard model is special. Beyond the standard model these
issues yield qualitative changes and affect such varied scenarios like
grand-unified theories, supersymmetry, and quantum gravity.
The talk provides an overview of the underlying mechanisms, including
some lattice results in their support, and finally highlights a few
example applications.