Cours gabriele veneziano

Particules Élémentaires, Gravitation et CosmologieAnnée 2004-2005Interactions fortes et chromodynamique quantique I:Aspects perturbatifsCours VIII: 19 avril 2005Symmetries & Anomalies1. Global vs. local symmetries2. Classical global symmetries, conserved currents3. Explicit breaking, accidental symmetries,anomalies4. Explicit vs. spontaneous symmetry breaking5. CP & U(1) problems in QCD19 avril 2005 1G. Veneziano, Cours no. 81. Global vs. local symmetries In QFT we have to make the important distinctionbetween global (rigid) and local symmetries Example of former is Lorentz(Poincaré) invariance Example of latter are the gauge symmetries(NB. General Relativity can be seen as a gaugetheory with G = local Poincaré-group: x -->x’(x)) Recall: local symmetries mean that some d.o.f. areunphysical => they are sacred (have to be broken«carefully» ) Global symmetries are not sacred: we are allowedto break them explicitly19 avril 2005 2G. Veneziano, Cours no. 8    Occasionally symmetries of S are broken at thecl quantum level (i.e. in S ). One talks about aneff«anomaly» We have seen an example all along: Classical-CDcontains no dimensionful parameter, but QCDcontains a scale, : one talks indeed about a scale-invariance (or trace) anomaly, anomalousdimensions etc. Anomalies are acceptable in global symmetries Anomalies unacceptable in local symmetries (animportant constraint on the standard model andits possible extensions)19 avril ...