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In order that the two components of the field ψ ( v )$_{L}$ behave as clearly identified U (1) -charged particles, it is necessary to have v ( 1 0 0 s 2 ) v − 1 diagonal. This is achieved only when 

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for constants α, β ∈ R . The case v = 1l$_{2}$ corresponds to α ≡ 0 mod 2 π . 

For any constant values α, β ∈ R , the field content of the obtained Lagrangians is exactly the same. These different theories are related by global transformations involving constant phases. For instance, using previous notations, one has ψ ( v )$_{L}$ = vψ ′ L = v ( ν$_{L}$ $_{e$_{L}$}$) , which relates fermions fields, and the previously mentioned relation B ( v )$_{µ}$ = vB$_{µ}$v − $^{1}$, which gets rid of the fields Z$_{µ}$ and W ± µ . Notice that if one does not require that the final fields behave correctly under U (1) -gauge transformations, any values of v are acceptable. 

The computation we have presented here is only based on a convenient change of variables at the classical level of the theory, given essentially by (2) and (3). It does not make any reference to some “broken vacuum” (fundamental configuration of φ ) which would be responsible for the (spontaneous) breaking of the symmetry. 

The most important outcome is that at the classical level the SU (2) symmetry is not broken: it is in fact factored out from the Lagrangian by this change of variables, as one would have expected in some gauge fixing procedure. The gauge group SU (2) is always there, but it does not effectively operate anymore on any fields . This really changes the point of view one has to have on this mechanism in the Standard Model: it looks more like an efficient gauge fixing procedure performed at the classical level than a symmetry breaking mechanism. 

It is well known that the quantization of the Standard Model is well behaved with the full Lagrangian (1), for which renormalizability has been established with success, using for instance the R$_{ξ}$ -gauge $^{6}$. On the contrary, the unitary gauge which is used in our computation is not suitable to construct a reliable perturbative renormalizable theory. Our computation does not seem to give any new light on the technical aspect of the quantization of the theory. 

Indeed, one can perform the change of variables presented here in the functional integral defining the quantized version of the theory, starting from the Lagrangian (1). Using the Jacobian of the change of variables from ( φ, b$_{µ}$, ψ$_{L}$ ) to ( U, η, B$_{µ}$, ψ ′ $_{L}$) (see Appendix A), one 

