A theorem on the Higgs sector of the Standard Model

We provide the solution of the classical theory for the Higgs sector of the Standard Model obtaining the exact Green function for the broken phase. Solving the Dyson-Schwinger equations for the Higgs field we show that the propagator coincides with that of the classical theory confirming the spectrum also at the quantum level. In this way we obtain a proof of triviality using the K\"allen-Lehman representation. This has as a consequence that higher excited states must exist for the Higgs particle, representing an internal spectrum for it. Higher excited states have exponentially smaller amplitudes and so, their production rates are significantly depressed.