Classical field theory

Special Relativity and Electrodynamics (Spring, 2012)

April 30, 2012

Professor Susskind moves on from relativity to introduce classical field theory. The most commonly studied classical field is the electromagnetic field; however, we will start with a less complex field - one in which the field values only depends on time - not on any spatial dimensions.

Professor Susskind reviews the action principle and the Lagrangian formulation of classical mechanics, and describes how they apply to fields. He then shows how the generalized classical Lagrangian results in a wave equation much like a multi-dimensional harmonic oscillator.

Next, professor Susskind brings in relativity and demonstrates how to create a Lorentz invariant action, which implies that the Lagrangian must be a scalar.

The lecture concludes with a discussion of how a particle interacts with a scalar field, and how the scalar field can give rise to a mass for an otherwise massless particle. This is the Higgs mass mechanism, and the simple time dependent field we started the lecture with is the Higgs field.

  • Introduction to classical field theory
  • Action and Lagrangian for a field in four-space
  • Continuum mechanics
  • Introducing relativity into the Lagrangian formulation for a field
  • Particle interacting with a simple scalar field
  • Higgs mechanism