# 2010 PDE2 Classical Field Theory

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## To Do List

1. Derive Scalar Field Equation in Minkowski background

2. Global to Local Symmetry Breaking and Maxwell's equations

• What are Maxwell's equations? Express them in tensor $F^{\mu \nu}$ notation and in differential forms (Cartan) $dF$ notation.
• Show that Maxwell's equations are hyperbolic; find the wave equation inside Maxwell's equations.

3. Lagrangian Formulation of the Field Equations in General Relativity.