Advanced concepts of theoretical physics (sketch)



Lecturer: Mikko Laine
Literature: H. Georgi, Lie algebras in particle physics
B.G. Wybourne, Classical groups for physicists
J.J. Sakurai, Modern quantum mechanics
R.P. Feynman and A.R. Hibbs, Quantum mechanics and path integrals
S. Coleman, Aspects of symmetry
R. Rajaraman, Solitons and instantons
Contents: 1: Group theory. Basic concepts.   Sheet 1.
2: Lie group vs Lie algebra.   Sheet 2.
3: Representations.   Sheet 3.
4: Weights and roots.   Sheet 4.
5: Classification of irreducible representations.   Sheet 5.
6: Reduction.   Sheet 6.
7: Lorentz group.   Sheet 7.
8: Global group properties.   Sheet 8.
9: Path integral. Review of basics.   Sheet 9.
10: Thermodynamics.   Sheet 10.
11: Saddle point and instantons.   Sheet 11.
12: Kind of a synthesis. Topological defects (vortices, monopoles).  
13: Topological gauge configurations (non-Abelian instantons, sphalerons).