- The Electromagnetic Field and Stress Energy Tensor
The most familiar example of a relativistic field theory is the electromagnetic field. We wish to think of the Maxwell equations as the Lagrange equations of a suitable Lagrangian. The aim is to find this suitable Lagrangian. Next by examining the symmetries of the Lagrangian we may write down conserved quantities via Noether’s theorem. But first we begin with a description of the relativistic nature of the electromagnetic field. We wish to convince the reader that hidden in the equations that describe everyday phenomena are the seeds of special relativity. Historically, the observation that these equations are not compatible with Galilean relativity is what led to the development of special relativity.