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Symmetries in Particle Physics

Symmetries are central to so much of physics. Noether’s theorem tells us that if a system has a continuous symmetry then it will have a corresponding conserved quantity. Goldstone’s theorem tells us that if a quantum field theory has a broken symmetry then it will possess a massless particle. Lorentz symmetry underpins special relativity and makes quantum field theory calculations much easier to work with. Continuous symmetries are formalised mathematically typically in terms of Lie groups and Lie algebras. These include the familiar cases of rotations and Lorentz transforms but extend to include the gauge groups of quantum field theory.

The Cambridge postgraduate mathematics masters, known as Part III, includes a course on this material, Symmetries in Particle Physics . In 2005 it was lectured by Dr Gutowski. It covered the following areas;

  •  Lie groups and Lie algebras
  • SU(2), SU(3), isospin and quarks
  • Space-time symmetries
  • Gauge theories

This is a fourth year course.

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