Advanced Quantum Mechanics
A reading course, 2006
Part A: Relativistic quantum mechanics
The Lorentz group, its four-dimensional representations, the infinitesimal generators and discrete pieces; Thomas rotations; two and three dimensions; tensors, direct products, irreducible representations; two-component spinor representations, building vectors and scalars from spinors.
The electromagnetic field tensor; the Bianchi identity; the action for the electromagnetic field; the field equations; gauge invariance, Noether's theorem and charge conservation.
The Klein-Gordon equation; free particle solutions; the probability current; the action principle for the Klein-Gordon field.
The Dirac equation; relations between the Dirac spinors and two-component spinors, tensor decomposition of Dirac bilinears; free particle solutions, representations of the Dirac matrices; P, T and C; non-relativistic reduction; the probability current, problems with the single particle, the Dirac sea; some problems.
Part B: Quantum mechanics of many particles
Sourendu Gupta: Created on Sep 2, 2006, last modified on Oct 12, 2006.