PX156 - I1 - symmetries

• particle physics is the physics of symmetries

• a symmetry is an operation on a system which leaves the system, the physics and/or the maths describing the system unchanged

• the maths governing symmetries like this is group theory

• types of symmetries

  • continuous: an infinite number of operation maps the system on to itself, ie: smoothly differentiable
    • eg: rotating a circle by $d\theta$
    • known as a lie group
  • discrete: a finite number of operation maps the system on to itself
    • eg: rotating a square by $90\mathrm{°}$
  • internal symmetries: changing the maths describing the system doesn't change the predictions

noether's theorem

• any system with a continuous, differentiable symmetry embodies an associated conservation law