has ∫ [ dφ ][ db$_{µ}$ ][ da$_{µ}$ ][ dψ$_{L}$ ][ dψ$_{R}$ ] e iS [ φ,b$_{µ}$,a$_{µ}$,ψ$_{L}$,ψ$_{R}$ ] = ∫ η $^{3}$[ dη ][ dU ][ dB$_{µ}$ ][ da$_{µ}$ ][ $_{dψ}$′ $_{L}$][ $_{dψ}$′ $_{R}$] e iS [ η,B$_{µ}$,a$_{µ}$,ψ ′ $_{L}$,ψ ′ $_{R}$] On the one hand, in the second expression the integration along the U fields over the gauge group SU (2) can be factored out because the action does not depend anymore of these fields. One step further, this remains true for the functional integral in the variables of the final Lagrangian (8), where the fields W ± µ , Z$_{µ}$ and A$_{µ}$ have been introduced. The “volume” of the gauge group SU (2) can then be factored out in the functional integral at the quantum level, as required by a gauge fixing procedure. But on the other hand, the presence of the term η 3 in the functional integral measure may be the sign that the quantization of the Higgs sector is non trivial with this final Lagrangian. Appendix A: Computation of the Jacobian For sake of completeness, we expose here the computation of the Jacobian arising in the functional integral for the change of variables ( φ, b, ψ$_{L}$ ) ↦→ ( U, η, B, ψ ′ $_{L}$) , where b = ( b$_{µ}$ ) and B = ( B$_{µ}$ ) . In fact, it is convenient to compute this Jacobian for the new variables ( U, σ, B, ψ ′ $_{L}$) where the new field σ is defined as η = e $^{σ}$. At the end, we will replace η [ dσ ] by [ dη ] . The change of variables between these fields is summarized in the following relations, where old fields are expressed in terms of new fields: φ = Ue σ   0 1   , ψ$_{L}$ = $_{Uψ}$′ $_{L}$, (A1) b$_{µ}$ = UB$_{µ}$$_{U}$− 1 + 2 i g U ( ∂$_{µ}$$_{U}$− $^{1}$) (A2) The functional spaces in which these fields are defined are given by: where underlined symbols are spaces of functions with values in the specified space, A is the space of su (2) -connection 1 -forms and S is the space of spinors. φ ∈ C 2 b, B ∈ A ψ$_{L}$$_{, ψ}$′ L ∈ S ⊗ C 2 U ∈ SU (2) σ ∈ R 13