# Advanced Quantum Mechanics

# A reading course, 2006

## Part A: Relativistic quantum mechanics

### Section 1

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.

### Section 2

The electromagnetic field tensor; the Bianchi identity; the action for the electromagnetic field; the field equations; gauge invariance, Noether's theorem and charge conservation.

### Section 3

The Klein-Gordon equation; free particle solutions; the probability current; the action principle for the Klein-Gordon field.

### Section 4

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.