Professor Susskind begins with a discussion of how, in the case of charged particle in an electromagnetic field, the particle affects the field and vice-versa. This effect arises from cross terms in the Lagrangian. He then derives the action, Lagrangian, and equations of motion for this case, and shows that the equations of motion are wave equations with a singularity at the location of the particle.

Professor Susskind then introduces the contravariant and covariant four-vector notation and Einstein's summation conventions used in the study of relativity.

He then proves that scalar Lagrangians are Lorentz invariant.

Finally, Professor Susskind solves the wave equation for a particle in a field and demonstrates that the solutions are sums of plane waves. The Higgs boson is the case of a charged particle with zero mass, and the resulting field derived from the equations solved here is the Higgs field. The Higgs field is the origin of the electron mass.

1. The Lorentz Transform
2. Adding Velocities
3. Relativistic Laws of Motion and E = mc2
4. Classical Field Theory
5. Particles and Fields
6. The Lorentz Force Law
7. The Fundamental Principles of Physical Laws
8. Maxwell's Equations
9. Lagrangian for Maxwell's Equations
10. Connection Between Classical Mechanics and Field Theory

In 1905, while only twenty-six years old, Albert Einstein published "On the Electrodynamics of Moving Bodies" and effectively extended classical laws of relativity to all laws of physics, even electrodynamics. In this course, we will take a close look at the special theory of relativity and also at classical field theory. Concepts addressed here will include four-dimensional space-time, electromagnetic fields, and Maxwell's equations.