The Dirac Equation

Introducing Spin

  1. The Stern-Gerlach experiment
  2. Spin vs. orbital angular momentum
  3. Connection to the Pauli-matrices
    One can represent a spin 1/2 ket (bra) by arranging the coefficients of an eigenket expansion in terms of |+> and |-> in a column (row) matrix also called a two-component spinor (Pauli, 1926):
    paulispinors
    Likewise one has
    paulispinorsconj
    The matrix elements <+-|Sk|+> and <+-|Sk|-> in this representation can be written in terms of 2x2 matrices (Pauli matrices):
    matrixlementswithpaulimatrices
    The expectation value for Sk is then given by
    expectationvaluewithpaulimatrices
    where
    paulimatrices
    The Pauli matrices have the following properties
    paulimatricesproperties1
    paulimatricesproperties2
  4. Fields with internal degrees of freedom: Isospin and Colour
  5. Example of isospin conservation