ABSTRACT
When the electron was first discovered, it was known to be a charged particle. It acted like a particle and could be weighed and examined as if it were a particle. De Broglie then proposed that the electron was in fact a manifestation of a matter wave. When the electromagnetic wave was discovered by Maxwell, light was then known to be a wave. It acted like a wave, and it was only Planck’s explanation of the photoelectric effect that led to the discovery of the photon. Schrodinger’s equation brought an uneasy relationship between the wave and particle duality of the electron, but Dirac’s relativistic treatment went further and implied the existence of a field – the quantum field. In order to understand the quantum field, we need to first understand the classical field, and in this chapter, the equations that describe a field are presented in terms of a very important quantity called the Lagrangian. The principle of least action, which makes use of the Lagrangian, is a result of classical field theory and is later shown to be fundamental to the motion of all sub-atomic particles.
