400nW Relativistic Quantum Mechanics: Course Outline (2011)
From the table of contents:
- Contents
- Introduction
- Notation
- Matrix Lie groups
- Definitions
- Parametrizing the Lie algebras, dimensions
- Orthogonal and unitary Lie-groups and algebras, a summary
- Representations, the fundamental and adjoint representations
- Representations of a Lie group
- Representations of a Lie algebra
- Examples of representations
- Exercises on group theory (warm up problems)
- From Galilei to Einstein
- Galilei invariance in classical mechanics
- On to special relativity
- The Lorentz and Poincaré groups
- Exercises on Lorentz transformations
- Physical invariants of interest
- The Klein-Gordon field - elements of field theory
- Relativistic quantum field theory and second quantization: why and what for
- Classical field theory
- Exercises on classical field theory
- The Klein-Gordon field in Hamiltonian quantization: Schrödinger picture and particle interpretation
- The Klein-Gordon field in space-time
- Heisenberg picture and time evolution
- Microscopic causality
- Complex fields and the starting point to a particle antiparticle interpretation
- Exercises on the quantized, free Klein-Gordon theory
- The interacting Klein-Gordon field: $\phi^4$-theory
- The S-matrix and time ordering
- Exercises on propagators and interacting theories
- Path-integrals for $\phi^4$-theory
- The idea of generating functionals
- The free theory
- The interacting theory
- First steps in perturbation theory
- Feynman rules in momentum space
- Scattering amplitudes and cross sections
- The Dirac equation and fermion fields
- SL(2,C) as the universal cover of SO(1,3)
- Constructing the Dirac equation
- Dirac Lagrangian, bilinear invariants and chiral symmetries
- Free particle solutions of the Dirac equation
- Quantization by anticommutators: fermions
- The Dirac propagator
- Classical gauge theory
- Abelian and nonabelian local gauge invariance
- The classical Higgs mechanism
- Remarks on polarization states in massive and massless QED
- The Higgs-Kibble model
- Solutions to (selected) exercises