Valery Zamiralov

Introduction to group theory and its representations and some applications to particle physics

I. Introduction

• Introduction
• Groups and algebras. Basic notions
• Representations of the Lie groups and algebras
• Unitary unimodular group SU(2)
• SU(2) as a spinor group
• Isospin group SU(2)
• Unitary symmetry group SU(3)

II. Unitary symmetry and quarks

• Eightfold way. Mass formulae in SU(3)
  • Baryon and meson unitary multiplets
  • Mass formulae for octet of pseudoscalar mesons
  • Mass formulae for octet of  baryons J^P = 1/2⁺
  • Nonet of the vector meson and mass formulae
  • Decuplet of baryon resonances with  J^P = 3/2⁺ and its mass formulae
• Praparticles and hypothesis of quarks
• Quark model. Mesons in quark model
• Charm and its arrival in particle physics
• The fifth quark. Beauty
• Truth or top?
• Baryons in quark model

III. Currents in unitary symmetry and quark models

• Electromagnetic current in the models of unitary symmetry and of quarks
  • On magnetic moments of barions
  • Radiative decays of  vector mesons
  • Leptonic decays of vector mesons V--> l⁺l^-
• Photon as a gauge field
• Rho-meson as a gauge field
• Vector and axial-vector currents in unitary symmetry and quark model
  • General remarks on weak interaction
  • Weak currents in unitary symmetry model
  • Weak currents in a quark model

IV. Introduction to Salam-Weinberg-Glashow model

• Neutral weak currents
  • GIM model
  • Construction of the Salam-Weinberg model
  • Six quark model and CKM matrix
• Vector bosons W and Y as gauge fields
• About Higgs mechanism

V. Colour and gluons

• Colour and its appearence in particle physics
  • Gluon as a gauge field
  • Simple examples with coloured quarks

VI. Conclusion