Physical observables in Brout-Englert-Higgs theories

We will use the method proposed by Fröhlich, Morchio, and Strocchi to analyze the spectrum of gauge theories with a Brout-Englert-Higgs mechanism. This formalism relates gauge-invariant bound state operators to invariant objects of the remaining unbroken gauge group after gauge fixing which provides a strict gauge-invariant formulation of the latter in terms of the original gauge symmetry without using the terminology of spontaneous gauge symmetry breaking. We also demonstrate that the Fröhlich-Morchio-Strocchi approach allows us to put new constraints on theories beyond the standard model by pure field-theoretical considerations and emphasize the exceptional role of the standard model weak gauge group. Particularly the conventional construction of grand unified theories has to be rethought.