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Heribert Weigert

Course Outline

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