Classical field theory

Sir William Rowan Hamilton

I really want to do section 4.3 the Lagrangian formulation of general relativity but first I am going back to section 1.10 on classical field theory which I skipped  because it involved the mysterious Lagrangian. I also needed to know about the fascinating Taylor expansions (Commentary 1.10 Taylor and Maclaurin series) and its extension for a function of two variables (which I guessed to begin with). My investigations on the Laplace operator or Laplacian (##\nabla^2## see Commentary 4.1 Laplacian) also came in handy.

Considering the number of things I did not know it was a good idea to postpone reading this section until now.

The section describes how we use Hamilton's least action principle and the Lagrangian which becomes the Lagrange density to get field equations.
It then has examples of how to use the procedure to get

• a scalar field theory, 
• a field theory for a harmonic oscillator which might be related to the relativistic equation of motion of an electron and 
• an Electro Magnetic field theory which (with some assumptions) gives Maxwell's equations.

The key thing is to guess the Lagrange density in each case .

Read about my chapter 1 "Endkampf" here: Commentary 1.10 Classical Field Theory.pdf (9 pages)