† jean-christophe.wallet@th.u-psud.fr 1 S. L. Glashow, Nucl. Phys. 22 , 579 (1961); S. Weinberg, Phys. Rev. Lett. 19 , 1264 (Nov 1967); A. Salam, in Elementary particle theory: relativistic groups and analyticity, Proceedings of the 8th Nobel Symposium , edited by N. Svartholm (Almquist and Forlag, Stockholm, 1968). 2 S. Weinberg, The Quantum Theory Of Fields: Modern Applications (Cambridge University Press, 2005); M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Perseus Books, 2008); I. J. R. Aitchison and A. J. G. Hey, Gauge Theories in Particle Physics - Vol. 2: Non-Abelien Gauge Theories: QCD and the Electroweak Theory (Institute of Physics Publishing, 2004); T.-P. Cheng and L.-F. Li, Gauge theory of elementary particle physics (Oxford University Press, 1984). 3 This is a known fact that the potential singularities of U at x such that η ( x ) = 0 can prevent this relation to be a gauge transformation, which indeed requires a smooth function with values in SU (2) . Nevertheless, the argument we stress here is at a more fundamental level. 4 C. Becchi, in Renormalization of Quantum Field Theories with Non-linear Field Transformations , Lecture Notes in Physics, Vol. 303 (Springer-Verlag, 1988) pp. 95–108; J. Zinn-Justin, Quantum Field Theory and Critical Phenomena , International Series of Monographs on Physics, Vol. 77 (Oxford Science Publications, 1990). 5 D. Bettinelli, R. Ferrari, and A. Quadri, Journal of Generalized Lie Theory and Applications 2 , 122 (2008); Physical Review D 77 , 045021 (2008); “The SU (2) ⊗ U (1) electroweak model based on the nonlinearly realized gauge group,” Preprint, http://arxiv.org/abs/0807.3882v3 . 6 G. ’t Hooft, Nucl. Phys. B 33 , 173 (1971); 35 , 167 (1971); G. ’t Hooft and M. Veltman, 44 , 189 (1972); 50 , 318 (1972). 16