On the semi-classical vacuum structure of the electroweak interaction

It is shown that in the semi-classical approximation of the electroweak sector of the standard model the moduli space of vacua can be identified with the first de Rham cohomology group of space–time. This gives a slightly different physical interpretation of the occurrence of the well-known Ahoronov–Bohm effect. Moreover, when charge conjugation is taken into account, the existence of a non-trivial ground state of the Higgs boson is shown to be equivalent to the triviality of the electroweak gauge bundle. As a consequence, the gauge bundle of the electromagnetic interaction must also be trivial. Though derived at “tree level” the results presented here may also have some consequences for quantizing, e.g., electromagnetism on an arbitrary curved space–time.