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.
- Non-relativistic limit for a particle in a field
- Einstein & Minkowski notation
- Wave equations for fields
- Klein-Gordon equation
- Higgs field
- Higgs boson