Conservation Laws in Relativistic Field Theory

Abstract

In sect. 5.9 we derived the conservation laws for energy and momentum of the electromagnetic field, with only a hint at angular momentum. In the present chapter we are going to show quite generally that conservation of energy, momentum, and angular momentum, as well as the law of motion for the center of mass(-energy) is intimately related to Poincare covariance of the Lagrangian formulation of the dynamics. More precisely, we shall be able to associate a divergence-free symmetric energy-momentum tensor with any physical system whose dynamics derives from a 'principle of stationary action' that is Poincare-covariant: translational covariance produces a divergence-free tensor, and rotational covariance allows to symmetrize it.