Maxwell’s Equations are Lorentz Invariant

Maxwell’s Equations

Charge current obeys continuity eqn. continuity equation, or charge conservation charge current density density

Charge current 4-vector Divergence operator is invariant under Lorentz transformations Define charge current 4-vector

E&M potentials Define scalar and vector potentials, and . this works because this works because and

The Lorenz condition How are and related? Lorenz condition: Its divergence is Lorentz invariant Define potential 4-vector

Wave equation for Use the first inhomogeneous eqn to show that obeys the wave equation, travelling at c.

Wave equation for Use the second inhomogeneous eqn to show that obeys the wave equation, travelling at c.

Maxwell’s equations in Lorentz invariant form

Maxwell’s Equations Used and to make a charge current 4-vector, Used and to make a scalar and vector potentials, and Used and to make a 4-potential,

E&M field tensor