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∗Équipe PTIDEJ– GEODES Département d’informatique et de recherche opérationnelle, Université de Montréal CP 6128 succ. Centre Ville, Montréal, Québec, H3C 3J7, Canada {mohanaou, foutsekh, guehene}@iro.umontreal.ca ∗∗ Équipe Adam – INRIA Futurs Université des Sciences et Technologies de Lille – LIFL UMR CNRS 8022 Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France {Laurence.Duchien, Anne-Fr...

OScLfet.v Reseanch 7leasn, Alationalbistitute ofAnimal Hbalth, MtRO, 3-1-5 Klinnondoi, Tkztkuba, Ibaraki 305-e856, ?JFletkushima Kenchu Livestock H}giene Set'viee CenteF, 1(bi'i.vama, Fukushima, 963-8041, S)Okinawa lnstitute of'Animal Health, A'aha, Okinan,a, 900-O024 and "Livestock 7lechnotogr) Research denter, IIiroshima Projleciural 7lechnologi, Researeh in,stittite, fiVtobara, U}roshima, 7...

Recall the global U(1) symmetry: Ψ→ e−ieΨ i.e. δΨ = −ieΨ. Let’s run the Noether argument: consider a slightly deformed, infinitesimal version of the symmetry transformation: Ψ→ Ψ + ρδΨ, where is just a small number to keep track of order, and ρ is some general function of x. The fact that we have a U(1) symmetry tells us the action must change under the deformed transformation by δS = ∫ dx J N∂...