DISCRETE AND GLOBAL SYMMETRIES IN PARTICLE PHYSICS
R.D. Peccei (UCLA)

I begin these lectures by reviewing the experimental status of various discrete space-time symmetries (C, P, T, CP and CPT), as well as of number conservation laws (lepton flavor number, L, B). I show next how one can qualitatively under- stand these results on the basis of the standard model. First, after describing how fields transform under discrete space-time symmetries, I sketch a proof of the CPT theorem. I then illustrate how the nature of the standard-model inter- actions lead naturally to P and C conservation (violation) in the strong and electromagnetic (weak) interactions. I also show how the lightness of neutrino masses can help account for the (near) conservation of leptonic flavor. How- ever, not all symmetries at the Lagrangian level are real symmetries of the theory, because of chiral anomalies. I show, in particular, how in the standard model anomalies lead to the violation of B + L in the electroweak theory and of U(1)A in (massless) QCD. The final part of the lectures focuses on four special topics related to discrete and global symmetries: i) the status of CPT tests in the Kaon system and the prospects for their improvement at a factory; ii) con- sequences of spontaneously broken global symmetries, leading to the existence of real Nambu-Goldstone bosons like Majorons or Familons; iii) the strong CP problem and spontaneously broken global chiral symmetries; iv) the issue of whether global symmetries can exist in the presence of gravitational inter- actions.

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