Lagrangian for Maxwell's equations

Special Relativity and Electrodynamics (Spring, 2012)

June 11, 2012

Professor Susskind begins the lecture by solving Maxwell's equations for electromagnetic plane waves. He then uses the principles of action, locality and Lorentz invariance to develop the Lagrangian for electrodynamics for the special case without charges or currents. Using the Euler-Lagrange equations with this Lagrangian, he derives Maxwell's equations for this special case. Finally, Professor Susskind adds the Lagrangian term for charges and currents by using the principle of gauge invariance, and again uses the Euler-Lagrange equations to derive Maxwell's equations in relativistic notation.

  • Electromagnetic plane waves
  • Choosing a Lagrangian for electrodynamics and deriving Maxwell's equations
  • Adding charges and currents to the Lagrangian