Fermions and the Dirac equation

Advanced Quantum Mechanics (Fall, 2013)

November 25, 2013

Professor Susskind closes the course with the presentation of the quantum field theory for spin-1/2 fermions.  This theory is based on the Dirac equation, which, when Dirac developed it in 1928, was the first thory to account fully for special relativity in the context of quantum mechanics.  This theory explains spin as a consequaence of of the union of quantum mechanics and relativity, and also led to the theory of antimatter and ultimate discovery of the first antimatter particle - the positron.

Professor Susskind begins the presentation by reviewing the Dirac equation for an electron in one dimension, and then generalizes this to derive the therory for three dimensions.  This led Dirac to develop his 4x4 gamma matrices.  In Dirac's theory, the mass of fermions originates from the cross term between the two chiralities in the Dirac equation.


  • Fermion
  • Dirac equation
  • Pauli matrices
  • Chirality
  • Dirac sea
  • Zitterbewegung
  • Positron