1. Professor Tony Leggett, UIUC
Spontaneous Symmetry Breaking: Its Successes, Its Limitations, and Its Pitfalls
Professor Tony Leggett, UIUC

2. Broken Symmetry
Hamiltonian (Lagrangian) of system is invariant under various symmetry operations.
Examples:
(1) Nonrelativistic CM system, e.g. gas of atoms of spin ½: (zero magnetic field)
invariant under: continuous discrete
spatial translation
rotn in orbital space
rotn in spin space
spatial inversion
time reversal
also (trivially) invariant under global “gauge transformation,
(2) QED Lagrangian (density):
invariant under: Poincaré group ( Lorentz + space-time transln), C, P, T, local gauge transfn