Classical field theory

Course goals

1. Generally derive field equations using the Lagrange and Hamilton formalism.
2. Derive conservation laws through Noether's theorem using system symmetries.
3. Describe actions and corresponding wave equations in a relativistic invariant way using four vectors.
4. Reproduce the Maxwell equations and the corresponding action covariant.
5. Apply the Maxwell equations to deduce the corresponding Green function.
6. Apply the Green function to solve the Maxwell equations for arbitrary time-dependent charge densities and charge current densities.
7. Apply the Green function to solve problems on radiation
8. Construct solitary-wave and solitonic solutions and discuss their properties for simple non-linear field equations

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