# Relativistic wave equation and conservation laws

### Special Relativity and Electrodynamics (Spring, 2008)

May 19, 2008

The conservation of charge relates to the mathematical statement of a vanishing divergence of the charge current. Study an example: the conservation of charge for a complex wave function. Conservation of charge can be derived using the infinitesimal change of phase of a complex wave function.

By “conserved” a physicist means there exists a

o current,

o conserved quantity and a

o continuity equation for the current and charge.

Isotopic spin has three components.

Study the relation between the energy and momentum of a particle.

Topics:

- Lorentz transformation
- Wave equation
- Classical field theory
- Complex wave function