After passing the course the student should be able to:
distinguish between gauge and global symmetries.
analyze the role of groups for generating symmetry transformations.
apply symmetry principles to quantum field theories.
account for basic concepts of spontaneous symmetry breaking.
find nontrivial solutions in quantum field theory.
Gauge and global symmetries, group theory applications to symmetries, non-Abelian gauge theories, spontaneous symmetry breaking and Goldstone’s theorem, the Breit-Englert-Higgs Effect. Nontrivial classical solutions: Kinks, vortices, Skyrmions and magnetic monopoles. Quantization of gauge fields, the Faddeev-Popov procedure and Ward identities, Becchi-Rouet-Stora-Tyutin (BRST) symmetry, supersymmetry.