procedure is beyond the scope of this paper and is under study. I. THE COMPUTATION Let us first fix the notations and ingredients which will be used in the following. We will restrict ourselves to the electroweak part of the Standard Model coupled to leptons and to only one flavor $^{1}$. Indeed, the computation can be easily generalized to the complete Standard Model without difficulty. For standard textbooks, see e.g. $^{2}$. Let us stress once again that in what follows, we will always stay at the classical level of the theory. The structure group is the usual U (1) × SU (2) . For a group G , we denote by G its gauge group, i.e. the group of smooth functions on space-time with values in G . The scalar Higgs fields doublet is denoted by φ = ( φ 1 φ 2 ) . Left fermions define a SU (2) -doublet ψ$_{L}$ of (left projected) Dirac spinors and the right fermion is a singlet ψ$_{R}$ , a (right projected) Dirac spinor. The gauge fields are denoted by a$_{µ}$ for the gauge group U (1) and b$_{µ}$ = b a $_{µ}$σ$_{a}$ for the gauge group SU (2) . Here the σ$_{a}$ ’s ( a = 1 , 2 , 3 ) are the standard Pauli matrices. The gauge fields are hermitean: a † µ = a$_{µ}$ and b † µ = b$_{µ}$ . The actions of the gauge groups U (1) and SU (2) on these fields are summarized in the following relations, with s ∈ U (1) and u ∈ SU (2) . In the following, we will always denote by s and u the U (1) and SU (2) gauge transformations. φ s = $_{s}$− $^{1}$φ φ u = $_{u}$− $^{1}$φ ψ s L = sψ$_{L}$ ψ u L = $_{u}$− $^{1}$ψ$_{L}$ ψ s R = s $^{2}$ψ$_{R}$ ψ u R = ψ$_{R}$ b s µ = b$_{µ}$ b u µ = $_{u}$− $^{1}$b$_{µ}$ u + 2 i g $_{u}$− $^{1}$∂$_{µ}$ u a s µ = a$_{µ}$ + 2 i g $_{$_{′}$s}$− $^{1}$∂$_{µ}$ s a u µ = a$_{µ}$ . The corresponding covariant derivatives are given by: D$_{µ}$φ = ( ∂$_{µ}$ − i g $_{2}$b$_{µ}$ − i g ′ 2 a$_{µ}$ ) φ D L $_{µ}$ψ$_{L}$ = ( ∂$_{µ}$ − i g $_{2}$b$_{µ}$ + i g ′ 2 a$_{µ}$ ) ψ$_{L}$ D R $_{µ}$ψ$_{R}$ = ( ∂$_{µ}$ + $_{ig}$′$_{a}$$_{µ}$$_{)}$$_{ψ}$$_{R}$ . 3