Abstract: 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 has been 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.